Poke holes in my grand-theory CFA
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Abel Dean
Aug 7, 2023, 2:17:41 PM8/7/23
to lavaan
Hello, all of you lavaan aficionados.
I would love it if you would poke holes in my confirmatory factor analysis. I think I found a general theory of plastic human differences, but you need to deflate my ego and tell me why it fails. If you do so or if you attempt to do so, then, if my work remains publishable, I will put your name FIRST in my acknowledgments. If my work becomes unpublishable because of your sharp-eyed review, then please suggest my reward for you.
My argument is that my CFA, with country-level cross-sectional indicators at 1995, including height (birth cohort of adults), BMI (body mass index at time of measurement), intelligence (IQ), and v-Loss (explained later), shows that the single general factor loads completely (0.99) on "v-Loss," defined as mortality weighted by reproductive value in proportion to concurrent raw mortality (and "reproductive value" or "v" is the weighting of each age class toward expected population growth: newborn females have moderate v, young adult females have greatest v, and postmenopausal females have no v). Not only is the loading near perfect, but so are the fit indices (rmsea.robust=0.000, rmsea.ci.upper.robust=0.095, pvalue.scaled=0.878, cfi.robust=1.000, srmr=0.001). Only the rmsea.ci.upper.robust is a near bust (should be <0.1), I expect due to the small sample (N=152 countries).
Only young people have reproductive value, and so my theory is that a bunch of trends of such human traits across the 20th century (people have been getting taller, fatter, smarter, and more) are caused by decreasing juvenile mortality (v-Loss), as the shared variation is predicted entirely by v-Loss, acting as the environmental cue along a plastic quantity-quality trade-off. So, instead of having MANY children, we are instead having FEWER children who are each developing faster and growing up to be more capable of survival.
You may have theoretical objections (i.e. fatter is higher quality?), but for here I am more interested in the quantitative technical problems.
I understand that a unitary factor loading is typically NOT evidence of a grand theory, but instead it would more likely be a hint that there was some blunder in the factor analysis. I expect there was no blunder, but I could be wrong.
One such possibility would have been overlap with the other indicators. But, only mortality and fertility feed into the calculation of v-Loss, which have nothing in common with intelligence, height and BMI.
Another possibility would have been overfitting. But, I can do cross validation with leave-1-out, leave-10-out, leave-25-out, or leave-76-out (slice the N randomly in half), and the results tend to be just as good. If I execute the leave-76-out ten times, then for eight out of ten executions the maximum rmsea.robust stays at 0.0000, and for the remaining two executions it is 0.0741 and 0.0899 (still within tolerance). If it is leave-1-out or leave-10-out, then I ALWAYS get rmsea.robust of 0.0000. If it is leave-25-out, then rmsea.robust is imperfect (0.0220) for only one execution out of ten.
So, please deflate my ego and find such a problem. Or, if you look and find nothing wrong, then please let me know that, too, not for the ego boost but just so I know that there are people looking--just tell me what you did, and, if it is valid potential problem that I did not think of, then I will still put you first in my acknowledgments. I don't want to submit this project to a journal without anyone looking for the obvious problems first.
It is also possible that there is nothing wrong except that the results were fished, fitting with that perfect loading and with those perfect or near-perfect fit indices only by random chance, which is possible, as this was an exploratory study, and, if so, there is no way to validate or invalidate it except by testing the same model on an independent dataset, and I expect I will get to that in a follow-up study, if I can find the necessary data. I am personally confident that this is not a matter of fishing, because I was about to settle on the mortality variable being deaths 0-28 years old in proportion to total deaths, which had the same loading and same excellent fit indices, but it had no basis in theory, and so I read up on life-history theory, found reproductive value, and I found that v-Loss correlated to that other mortality variable almost perfectly (r=0.98). But, I can not prove to anyone else that exploratory sequence, and that's why I say, "personally confident."
And, I won't argue about the validity of the country-level IQ data (Lynn & Vanhanen, 2012). I know it is controversial, but it is tentatively accepted by the relevant psychometricians (I went to their conference in Berkeley a couple weeks ago for a poster presentation), and arguing about it here in this group would be too much of a red herring.
For now, my best guess is that the df=1 is a problem. It isn't zero, but it is still too small for comfort, and I am not sure how serious that problem is.
My R script and data are downloadable as a single zip file here: https://figshare.com/s/16336698b040885a4ca1
That and my manuscript are accessible at the bottom of the page of this link here: https://figshare.com/projects/Possibly_explaining_plastic_human_differences_across_time_geography_and_disciplines/150987
I will be happy to help anyone who has any questions.
Thank you,
Mr. (not Dr.) Abel Dean
I would love it if you would poke holes in my confirmatory factor analysis. I think I found a general theory of plastic human differences, but you need to deflate my ego and tell me why it fails. If you do so or if you attempt to do so, then, if my work remains publishable, I will put your name FIRST in my acknowledgments. If my work becomes unpublishable because of your sharp-eyed review, then please suggest my reward for you.
My argument is that my CFA, with country-level cross-sectional indicators at 1995, including height (birth cohort of adults), BMI (body mass index at time of measurement), intelligence (IQ), and v-Loss (explained later), shows that the single general factor loads completely (0.99) on "v-Loss," defined as mortality weighted by reproductive value in proportion to concurrent raw mortality (and "reproductive value" or "v" is the weighting of each age class toward expected population growth: newborn females have moderate v, young adult females have greatest v, and postmenopausal females have no v). Not only is the loading near perfect, but so are the fit indices (rmsea.robust=0.000, rmsea.ci.upper.robust=0.095, pvalue.scaled=0.878, cfi.robust=1.000, srmr=0.001). Only the rmsea.ci.upper.robust is a near bust (should be <0.1), I expect due to the small sample (N=152 countries).
Only young people have reproductive value, and so my theory is that a bunch of trends of such human traits across the 20th century (people have been getting taller, fatter, smarter, and more) are caused by decreasing juvenile mortality (v-Loss), as the shared variation is predicted entirely by v-Loss, acting as the environmental cue along a plastic quantity-quality trade-off. So, instead of having MANY children, we are instead having FEWER children who are each developing faster and growing up to be more capable of survival.
You may have theoretical objections (i.e. fatter is higher quality?), but for here I am more interested in the quantitative technical problems.
I understand that a unitary factor loading is typically NOT evidence of a grand theory, but instead it would more likely be a hint that there was some blunder in the factor analysis. I expect there was no blunder, but I could be wrong.
One such possibility would have been overlap with the other indicators. But, only mortality and fertility feed into the calculation of v-Loss, which have nothing in common with intelligence, height and BMI.
Another possibility would have been overfitting. But, I can do cross validation with leave-1-out, leave-10-out, leave-25-out, or leave-76-out (slice the N randomly in half), and the results tend to be just as good. If I execute the leave-76-out ten times, then for eight out of ten executions the maximum rmsea.robust stays at 0.0000, and for the remaining two executions it is 0.0741 and 0.0899 (still within tolerance). If it is leave-1-out or leave-10-out, then I ALWAYS get rmsea.robust of 0.0000. If it is leave-25-out, then rmsea.robust is imperfect (0.0220) for only one execution out of ten.
So, please deflate my ego and find such a problem. Or, if you look and find nothing wrong, then please let me know that, too, not for the ego boost but just so I know that there are people looking--just tell me what you did, and, if it is valid potential problem that I did not think of, then I will still put you first in my acknowledgments. I don't want to submit this project to a journal without anyone looking for the obvious problems first.
It is also possible that there is nothing wrong except that the results were fished, fitting with that perfect loading and with those perfect or near-perfect fit indices only by random chance, which is possible, as this was an exploratory study, and, if so, there is no way to validate or invalidate it except by testing the same model on an independent dataset, and I expect I will get to that in a follow-up study, if I can find the necessary data. I am personally confident that this is not a matter of fishing, because I was about to settle on the mortality variable being deaths 0-28 years old in proportion to total deaths, which had the same loading and same excellent fit indices, but it had no basis in theory, and so I read up on life-history theory, found reproductive value, and I found that v-Loss correlated to that other mortality variable almost perfectly (r=0.98). But, I can not prove to anyone else that exploratory sequence, and that's why I say, "personally confident."
And, I won't argue about the validity of the country-level IQ data (Lynn & Vanhanen, 2012). I know it is controversial, but it is tentatively accepted by the relevant psychometricians (I went to their conference in Berkeley a couple weeks ago for a poster presentation), and arguing about it here in this group would be too much of a red herring.
For now, my best guess is that the df=1 is a problem. It isn't zero, but it is still too small for comfort, and I am not sure how serious that problem is.
My R script and data are downloadable as a single zip file here: https://figshare.com/s/16336698b040885a4ca1
That and my manuscript are accessible at the bottom of the page of this link here: https://figshare.com/projects/Possibly_explaining_plastic_human_differences_across_time_geography_and_disciplines/150987
I will be happy to help anyone who has any questions.
Thank you,
Mr. (not Dr.) Abel Dean
Abel Dean
Aug 7, 2023, 3:10:26 PM8/7/23
to lavaan
And, here is a lavaanPlot of that CFA, so you have a better idea of what I am talking about. You can see that I included a correlated error between height and BMI.
And, here is a long console output with many functions:
Begin time is: 20230807_133156.
Highlight the HumanDifferences folder and click OK.
Custom year = 1995; correlation type = spearman; custom estimator = MLR.
Importing the data.
Executing toggleProcessDeaths.
Executing toggleProcessGdppc.
Executing toggleProcessvLoss.
Executing toggleProcessMaster.
Executing toggleCfa.
CFA fit summary:
lavaan 0.6.16 ended normally after 24 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 13
Used Total
Number of observations 152 223
Model Test User Model:
Standard Scaled
Test Statistic 0.018 0.024
Degrees of freedom 1 1
P-value (Chi-square) 0.894 0.878
Scaling correction factor 0.757
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 401.364 273.741
Degrees of freedom 6 6
P-value 0.000 0.000
Scaling correction factor 1.466
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.015 1.022
Robust Comparative Fit Index (CFI) 1.000
Robust Tucker-Lewis Index (TLI) 1.011
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -648.312 -648.312
Scaling correction factor 1.120
for the MLR correction
Loglikelihood unrestricted model (H1) -648.303 -648.303
Scaling correction factor 1.094
for the MLR correction
Akaike (AIC) 1322.625 1322.625
Bayesian (BIC) 1361.935 1361.935
Sample-size adjusted Bayesian (SABIC) 1320.790 1320.790
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.100 0.000
P-value H_0: RMSEA <= 0.050 0.912 0.837
P-value H_0: RMSEA >= 0.080 0.065 0.130
Robust RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.095
P-value H_0: Robust RMSEA <= 0.050 0.905
P-value H_0: Robust RMSEA >= 0.080 0.064
Standardized Root Mean Square Residual:
SRMR 0.001 0.001
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
QuantityQuality =~
vLoss 1.000 0.962 0.987
Height -0.885 0.061 -14.557 0.000 -0.852 -0.836
Intelligence -0.782 0.056 -13.907 0.000 -0.753 -0.756
BMI -0.672 0.050 -13.518 0.000 -0.646 -0.699
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Height ~~
.BMI 0.052 0.049 1.065 0.287 0.052 0.141
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.vLoss -0.068 0.079 -0.855 0.392 -0.068 -0.069
.Height 0.131 0.083 1.585 0.113 0.131 0.129
.Intelligence -0.017 0.081 -0.206 0.837 -0.017 -0.017
.BMI 0.070 0.075 0.936 0.349 0.070 0.076
QuantityQualty 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.vLoss 0.024 0.039 0.602 0.547 0.024 0.025
.Height 0.312 0.052 5.968 0.000 0.312 0.301
.Intelligence 0.424 0.077 5.532 0.000 0.424 0.428
.BMI 0.438 0.077 5.691 0.000 0.438 0.511
QuantityQualty 0.926 0.082 11.230 0.000 1.000 1.000
R-Square:
Estimate
vLoss 0.975
Height 0.699
Intelligence 0.572
BMI 0.489
CFA fit indices:
npar fmin chisq df
13.000 0.000 0.018 1.000
pvalue chisq.scaled df.scaled pvalue.scaled
0.894 0.024 1.000 0.878
chisq.scaling.factor baseline.chisq baseline.df baseline.pvalue
0.757 401.364 6.000 0.000
baseline.chisq.scaled baseline.df.scaled baseline.pvalue.scaled baseline.chisq.scaling.factor
273.741 6.000 0.000 1.466
cfi tli cfi.scaled tli.scaled
1.000 1.015 1.000 1.022
cfi.robust tli.robust nnfi rfi
1.000 1.011 1.015 1.000
nfi pnfi ifi rni
1.000 0.167 1.002 1.002
nnfi.scaled rfi.scaled nfi.scaled pnfi.scaled
1.022 0.999 1.000 0.167
ifi.scaled rni.scaled nnfi.robust rni.robust
1.004 1.004 1.011 1.002
logl unrestricted.logl aic bic
-648.312 -648.303 1322.625 1361.935
ntotal bic2 scaling.factor.h1 scaling.factor.h0
152.000 1320.790 1.094 1.120
rmsea rmsea.ci.lower rmsea.ci.upper rmsea.ci.level
0.000 0.000 0.100 0.900
rmsea.pvalue rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
0.912 0.050 0.065 0.080
rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled rmsea.pvalue.scaled
0.000 0.000 0.000 0.837
rmsea.notclose.pvalue.scaled rmsea.robust rmsea.ci.lower.robust rmsea.ci.upper.robust
0.130 0.000 0.000 0.095
rmsea.pvalue.robust rmsea.notclose.pvalue.robust rmr rmr_nomean
0.905 0.064 0.001 0.001
srmr srmr_bentler srmr_bentler_nomean crmr
0.001 0.001 0.001 0.001
crmr_nomean srmr_mplus srmr_mplus_nomean cn_05
0.002 0.001 0.001 32800.066
cn_01 gfi agfi pgfi
56650.940 1.000 0.999 0.071
mfi ecvi
1.003 0.171
CFA parameter estimates:
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all std.nox
1 QuantityQuality =~ vLoss 1.000 0.000 NA NA 1.000 1.000 0.962 0.987 0.987
2 QuantityQuality =~ Height -0.885 0.061 -14.557 0.000 -1.004 -0.766 -0.852 -0.836 -0.836
3 QuantityQuality =~ Intelligence -0.782 0.056 -13.907 0.000 -0.893 -0.672 -0.753 -0.756 -0.756
4 QuantityQuality =~ BMI -0.672 0.050 -13.518 0.000 -0.769 -0.574 -0.646 -0.699 -0.699
5 Height ~~ BMI 0.052 0.049 1.065 0.287 -0.044 0.148 0.052 0.141 0.141
6 vLoss ~~ vLoss 0.024 0.039 0.602 0.547 -0.053 0.101 0.024 0.025 0.025
7 Height ~~ Height 0.312 0.052 5.968 0.000 0.210 0.415 0.312 0.301 0.301
8 Intelligence ~~ Intelligence 0.424 0.077 5.532 0.000 0.273 0.574 0.424 0.428 0.428
9 BMI ~~ BMI 0.438 0.077 5.691 0.000 0.287 0.588 0.438 0.511 0.511
10 QuantityQuality ~~ QuantityQuality 0.926 0.082 11.230 0.000 0.764 1.088 1.000 1.000 1.000
11 vLoss ~1 -0.068 0.079 -0.855 0.392 -0.223 0.087 -0.068 -0.069 -0.069
12 Height ~1 0.131 0.083 1.585 0.113 -0.031 0.293 0.131 0.129 0.129
13 Intelligence ~1 -0.017 0.081 -0.206 0.837 -0.175 0.142 -0.017 -0.017 -0.017
14 BMI ~1 0.070 0.075 0.936 0.349 -0.077 0.217 0.070 0.076 0.076
15 QuantityQuality ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
16 vLoss r2 vLoss 0.975 NA NA NA NA NA NA NA NA
17 Height r2 Height 0.699 NA NA NA NA NA NA NA NA
18 Intelligence r2 Intelligence 0.572 NA NA NA NA NA NA NA NA
19 BMI r2 BMI 0.489 NA NA NA NA NA NA NA NA
CFA VIF:
40.111
3.325
2.338
1.955
CFA more fit indices:
χ²/df = 0.0235
CFA residuals:
vLoss Height Intllg BMI
vLoss 0.000
Height 0.000 0.000
Intelligence 0.000 -0.002 0.000
BMI 0.000 0.000 0.004 0.000
CFA factor loadings with confidence intervals:
Latent Factor Indicator Loadings sig p Lower.CI Upper.CI SE z
1 QuantityQuality vLoss 0.987 *** 0 0.946 1.029 0.021 46.774
2 QuantityQuality Height -0.836 *** 0 -0.894 -0.779 0.029 -28.561
3 QuantityQuality Intelligence -0.756 *** 0 -0.844 -0.669 0.045 -16.961
4 QuantityQuality BMI -0.699 *** 0 -0.793 -0.605 0.048 -14.512
Many CFA models, one per column:
Var, param, fit CFA1 CFA2 CFA3 CFA4 CFA5 CFA6 CFA7 CFA8
v-Loss -0.939 -0.926 -0.948 -0.959 -0.975 NA -0.972 -0.987
CBR -0.939 NA NA NA -0.947 -0.982 NA NA
LifeExpec65 0.748 0.775 0.796 NA NA NA NA NA
Height 0.869 0.863 0.824 0.845 0.840 0.799 0.851 0.836
GDPpc 0.835 0.874 0.833 0.801 NA NA NA NA
Intelligence 0.822 0.804 0.783 0.774 0.784 0.803 0.764 0.756
LowBirthw -0.787 -0.788 NA NA NA NA NA NA
AgeMenar -0.618 -0.605 NA NA NA NA NA NA
BMI 0.671 0.712 0.731 0.733 0.681 0.604 0.715 0.699
AgeMenop 0.578 0.546 NA NA NA NA NA NA
Height~~BMI 0.375 0.300 0.087 0.044 0.171 0.328 NA 0.141
Scree factors 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
N obs. 42.000 42.000 149.000 149.000 152.000 152.000 152.000 152.000
Model df 34.000 26.000 8.000 4.000 4.000 1.000 2.000 1.000
Model χ² 70.913 61.543 72.875 23.802 23.113 2.804 1.726 0.024
Model p (≥.05) 0.000 0.000 0.000 0.000 0.000 0.094 0.422 0.878
RMSEA ε (≤.05) 0.164 0.175 0.219 0.163 0.186 0.100 0.000 0.000
ε lo90%CI (=0) 0.110 0.119 0.175 0.104 0.117 0.000 0.000 0.000
ε up90%CI(<.1) 0.217 0.232 0.267 0.230 0.263 0.247 0.164 0.095
p ε≤.05 (≥.05) 0.001 0.001 0.000 0.002 0.001 0.167 0.533 0.905
CFI (≥.95) 0.895 0.883 0.919 0.970 0.970 0.996 1.000 1.000
SRMR (≤.1) 0.059 0.059 0.040 0.028 0.019 0.013 0.011 0.001
Executing toggleCorTableForPaper.
Executing toggleCrossValidation.
Leave-25-out cross validation.
CFA mean rmsea.robust across 7 folds: 0.0000.
CFA SD of rmsea.robust across 7 folds: 0.0000.
CFA max rmsea.robust across 7 folds: 0.0000.
CFA mean rmsea.ci.upper.robust across 7 folds: 0.0935.
CFA SD of rmsea.ci.upper.robust across 7 folds: 0.0727.
CFA max rmsea.ci.upper.robust across 7 folds: 0.1815.
Custom year = 1995; correlation type = spearman; custom estimator = MLR.
End time is: 20230807_133214
Highlight the HumanDifferences folder and click OK.
Custom year = 1995; correlation type = spearman; custom estimator = MLR.
Importing the data.
Executing toggleProcessDeaths.
Executing toggleProcessGdppc.
Executing toggleProcessvLoss.
Executing toggleProcessMaster.
Executing toggleCfa.
CFA fit summary:
lavaan 0.6.16 ended normally after 24 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 13
Used Total
Number of observations 152 223
Model Test User Model:
Standard Scaled
Test Statistic 0.018 0.024
Degrees of freedom 1 1
P-value (Chi-square) 0.894 0.878
Scaling correction factor 0.757
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 401.364 273.741
Degrees of freedom 6 6
P-value 0.000 0.000
Scaling correction factor 1.466
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.015 1.022
Robust Comparative Fit Index (CFI) 1.000
Robust Tucker-Lewis Index (TLI) 1.011
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -648.312 -648.312
Scaling correction factor 1.120
for the MLR correction
Loglikelihood unrestricted model (H1) -648.303 -648.303
Scaling correction factor 1.094
for the MLR correction
Akaike (AIC) 1322.625 1322.625
Bayesian (BIC) 1361.935 1361.935
Sample-size adjusted Bayesian (SABIC) 1320.790 1320.790
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.100 0.000
P-value H_0: RMSEA <= 0.050 0.912 0.837
P-value H_0: RMSEA >= 0.080 0.065 0.130
Robust RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.095
P-value H_0: Robust RMSEA <= 0.050 0.905
P-value H_0: Robust RMSEA >= 0.080 0.064
Standardized Root Mean Square Residual:
SRMR 0.001 0.001
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
QuantityQuality =~
vLoss 1.000 0.962 0.987
Height -0.885 0.061 -14.557 0.000 -0.852 -0.836
Intelligence -0.782 0.056 -13.907 0.000 -0.753 -0.756
BMI -0.672 0.050 -13.518 0.000 -0.646 -0.699
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Height ~~
.BMI 0.052 0.049 1.065 0.287 0.052 0.141
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.vLoss -0.068 0.079 -0.855 0.392 -0.068 -0.069
.Height 0.131 0.083 1.585 0.113 0.131 0.129
.Intelligence -0.017 0.081 -0.206 0.837 -0.017 -0.017
.BMI 0.070 0.075 0.936 0.349 0.070 0.076
QuantityQualty 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.vLoss 0.024 0.039 0.602 0.547 0.024 0.025
.Height 0.312 0.052 5.968 0.000 0.312 0.301
.Intelligence 0.424 0.077 5.532 0.000 0.424 0.428
.BMI 0.438 0.077 5.691 0.000 0.438 0.511
QuantityQualty 0.926 0.082 11.230 0.000 1.000 1.000
R-Square:
Estimate
vLoss 0.975
Height 0.699
Intelligence 0.572
BMI 0.489
CFA fit indices:
npar fmin chisq df
13.000 0.000 0.018 1.000
pvalue chisq.scaled df.scaled pvalue.scaled
0.894 0.024 1.000 0.878
chisq.scaling.factor baseline.chisq baseline.df baseline.pvalue
0.757 401.364 6.000 0.000
baseline.chisq.scaled baseline.df.scaled baseline.pvalue.scaled baseline.chisq.scaling.factor
273.741 6.000 0.000 1.466
cfi tli cfi.scaled tli.scaled
1.000 1.015 1.000 1.022
cfi.robust tli.robust nnfi rfi
1.000 1.011 1.015 1.000
nfi pnfi ifi rni
1.000 0.167 1.002 1.002
nnfi.scaled rfi.scaled nfi.scaled pnfi.scaled
1.022 0.999 1.000 0.167
ifi.scaled rni.scaled nnfi.robust rni.robust
1.004 1.004 1.011 1.002
logl unrestricted.logl aic bic
-648.312 -648.303 1322.625 1361.935
ntotal bic2 scaling.factor.h1 scaling.factor.h0
152.000 1320.790 1.094 1.120
rmsea rmsea.ci.lower rmsea.ci.upper rmsea.ci.level
0.000 0.000 0.100 0.900
rmsea.pvalue rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
0.912 0.050 0.065 0.080
rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled rmsea.pvalue.scaled
0.000 0.000 0.000 0.837
rmsea.notclose.pvalue.scaled rmsea.robust rmsea.ci.lower.robust rmsea.ci.upper.robust
0.130 0.000 0.000 0.095
rmsea.pvalue.robust rmsea.notclose.pvalue.robust rmr rmr_nomean
0.905 0.064 0.001 0.001
srmr srmr_bentler srmr_bentler_nomean crmr
0.001 0.001 0.001 0.001
crmr_nomean srmr_mplus srmr_mplus_nomean cn_05
0.002 0.001 0.001 32800.066
cn_01 gfi agfi pgfi
56650.940 1.000 0.999 0.071
mfi ecvi
1.003 0.171
CFA parameter estimates:
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all std.nox
1 QuantityQuality =~ vLoss 1.000 0.000 NA NA 1.000 1.000 0.962 0.987 0.987
2 QuantityQuality =~ Height -0.885 0.061 -14.557 0.000 -1.004 -0.766 -0.852 -0.836 -0.836
3 QuantityQuality =~ Intelligence -0.782 0.056 -13.907 0.000 -0.893 -0.672 -0.753 -0.756 -0.756
4 QuantityQuality =~ BMI -0.672 0.050 -13.518 0.000 -0.769 -0.574 -0.646 -0.699 -0.699
5 Height ~~ BMI 0.052 0.049 1.065 0.287 -0.044 0.148 0.052 0.141 0.141
6 vLoss ~~ vLoss 0.024 0.039 0.602 0.547 -0.053 0.101 0.024 0.025 0.025
7 Height ~~ Height 0.312 0.052 5.968 0.000 0.210 0.415 0.312 0.301 0.301
8 Intelligence ~~ Intelligence 0.424 0.077 5.532 0.000 0.273 0.574 0.424 0.428 0.428
9 BMI ~~ BMI 0.438 0.077 5.691 0.000 0.287 0.588 0.438 0.511 0.511
10 QuantityQuality ~~ QuantityQuality 0.926 0.082 11.230 0.000 0.764 1.088 1.000 1.000 1.000
11 vLoss ~1 -0.068 0.079 -0.855 0.392 -0.223 0.087 -0.068 -0.069 -0.069
12 Height ~1 0.131 0.083 1.585 0.113 -0.031 0.293 0.131 0.129 0.129
13 Intelligence ~1 -0.017 0.081 -0.206 0.837 -0.175 0.142 -0.017 -0.017 -0.017
14 BMI ~1 0.070 0.075 0.936 0.349 -0.077 0.217 0.070 0.076 0.076
15 QuantityQuality ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
16 vLoss r2 vLoss 0.975 NA NA NA NA NA NA NA NA
17 Height r2 Height 0.699 NA NA NA NA NA NA NA NA
18 Intelligence r2 Intelligence 0.572 NA NA NA NA NA NA NA NA
19 BMI r2 BMI 0.489 NA NA NA NA NA NA NA NA
CFA VIF:
40.111
3.325
2.338
1.955
CFA more fit indices:
χ²/df = 0.0235
CFA residuals:
vLoss Height Intllg BMI
vLoss 0.000
Height 0.000 0.000
Intelligence 0.000 -0.002 0.000
BMI 0.000 0.000 0.004 0.000
CFA factor loadings with confidence intervals:
Latent Factor Indicator Loadings sig p Lower.CI Upper.CI SE z
1 QuantityQuality vLoss 0.987 *** 0 0.946 1.029 0.021 46.774
2 QuantityQuality Height -0.836 *** 0 -0.894 -0.779 0.029 -28.561
3 QuantityQuality Intelligence -0.756 *** 0 -0.844 -0.669 0.045 -16.961
4 QuantityQuality BMI -0.699 *** 0 -0.793 -0.605 0.048 -14.512
Many CFA models, one per column:
Var, param, fit CFA1 CFA2 CFA3 CFA4 CFA5 CFA6 CFA7 CFA8
v-Loss -0.939 -0.926 -0.948 -0.959 -0.975 NA -0.972 -0.987
CBR -0.939 NA NA NA -0.947 -0.982 NA NA
LifeExpec65 0.748 0.775 0.796 NA NA NA NA NA
Height 0.869 0.863 0.824 0.845 0.840 0.799 0.851 0.836
GDPpc 0.835 0.874 0.833 0.801 NA NA NA NA
Intelligence 0.822 0.804 0.783 0.774 0.784 0.803 0.764 0.756
LowBirthw -0.787 -0.788 NA NA NA NA NA NA
AgeMenar -0.618 -0.605 NA NA NA NA NA NA
BMI 0.671 0.712 0.731 0.733 0.681 0.604 0.715 0.699
AgeMenop 0.578 0.546 NA NA NA NA NA NA
Height~~BMI 0.375 0.300 0.087 0.044 0.171 0.328 NA 0.141
Scree factors 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
N obs. 42.000 42.000 149.000 149.000 152.000 152.000 152.000 152.000
Model df 34.000 26.000 8.000 4.000 4.000 1.000 2.000 1.000
Model χ² 70.913 61.543 72.875 23.802 23.113 2.804 1.726 0.024
Model p (≥.05) 0.000 0.000 0.000 0.000 0.000 0.094 0.422 0.878
RMSEA ε (≤.05) 0.164 0.175 0.219 0.163 0.186 0.100 0.000 0.000
ε lo90%CI (=0) 0.110 0.119 0.175 0.104 0.117 0.000 0.000 0.000
ε up90%CI(<.1) 0.217 0.232 0.267 0.230 0.263 0.247 0.164 0.095
p ε≤.05 (≥.05) 0.001 0.001 0.000 0.002 0.001 0.167 0.533 0.905
CFI (≥.95) 0.895 0.883 0.919 0.970 0.970 0.996 1.000 1.000
SRMR (≤.1) 0.059 0.059 0.040 0.028 0.019 0.013 0.011 0.001
Executing toggleCorTableForPaper.
Executing toggleCrossValidation.
Leave-25-out cross validation.
CFA mean rmsea.robust across 7 folds: 0.0000.
CFA SD of rmsea.robust across 7 folds: 0.0000.
CFA max rmsea.robust across 7 folds: 0.0000.
CFA mean rmsea.ci.upper.robust across 7 folds: 0.0935.
CFA SD of rmsea.ci.upper.robust across 7 folds: 0.0727.
CFA max rmsea.ci.upper.robust across 7 folds: 0.1815.
Custom year = 1995; correlation type = spearman; custom estimator = MLR.
End time is: 20230807_133214
Ibrahim Nasser
Aug 7, 2023, 3:27:32 PM8/7/23
to lav...@googlegroups.com
Your indicators are obviously composites. Do height and intelligence have a strong positive correlation? Have you forgotten about age, or why is that?
Ibrahim
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Ibrahim Nasser
Aug 7, 2023, 3:34:47 PM8/7/23
to lav...@googlegroups.com
Same for BMI. Age, height and weight are part of the calculation. I don't think your measurement model is useful Firma factor model.
Ibrahim
Abel Dean
Aug 7, 2023, 3:43:16 PM8/7/23
to lavaan
"Your indicators are obviously composites."
BMI is a composite across ages, I believe (sourced from the NCD-RisC Factor Collaboration). Height is just a mean."Do height and intelligence have a strong positive correlation?"
It is a Spearman's country-level correlation of r=0.68. All such traits correlate, but nobody knows why, beyond (uselessly) "wealth." This correlation table will help further:
With v-Loss and height, the correlation is -0.82. Such strengths of the correlations are strong but not enough, I expect, to predict a unitary loading on v-Loss. I could be wrong, so maybe you can convince me of that.
With v-Loss and height, the correlation is -0.82. Such strengths of the correlations are strong but not enough, I expect, to predict a unitary loading on v-Loss. I could be wrong, so maybe you can convince me of that.
"Have you forgotten about age, or why is that?"
Height is adult height, BMI is a composite, IQ is normed to each age group and is consistent across the whole lifespan (except with more variation in childhood), and v-Loss is a combination across age classes.
"I don't think your measurement model is useful Firma factor model."
Excuse me--what is a Firma factor model? Typo?
Thank you for taking a look, one way or the other! Please, follow up.
Abel Dean
Ibrahim Nasser
Aug 7, 2023, 3:55:03 PM8/7/23
to lav...@googlegroups.com
Height seems to be the only indicator that is not a composite. I consider a strong positive correlation between height and intelligence to be a spurious correlation. The model may fit very well. I think it is a largely misspecified model and the reason is that you use composites as measurement variables, which share common causes like age).
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Abel Dean
Aug 7, 2023, 4:08:42 PM8/7/23
to lavaan
"I consider a strong positive correlation between height and intelligence to be a spurious correlation."
The country-level correlation between height and intelligence is not spurious, whatever the explanation for it or whatever the common cause linking those two variables. The relationship exists on the individual level, too, though weaker. People in more developed countries are taller, and it also fits the secular trend of increasing height (we are giants compared to people of 1800).
"I think it is a largely misspecified model and the reason is that you use composites as measurement variables, which share common causes like age)."
But, the calcs for the composites removed the effect of age on the variation within three of the four indicators. The numbers would not be expected to change if the age structures of the populations changed, for either intelligence, height or BMI. Only v-Loss would vary with population age structure.
So, while I don't agree with that criticism, it still seems like it would be an objection good enough to address in my manuscript, so I would love to have your full name, and I will put you among the first in the acknowledgments. Thank you!
Abel
Ibrahim Nasser
Aug 7, 2023, 4:17:17 PM8/7/23
to lav...@googlegroups.com, Abel Dean
"we are giants compared to people of 1800". With that, you have proven yourself wrong. You asked for feedback and you got feedback.Maybe some kind of composite approach would be a better choice - Ibrahim
Jeremy Miles
Aug 7, 2023, 4:20:50 PM8/7/23
to lav...@googlegroups.com
' but nobody knows why, beyond (uselessly) "wealth." '??
It's very clear why. It's wealth. Why is this useless?
If a country gets richer, the people eat better, they grow larger, their BMI increases, child mortality drops, low birthweight drops, etc.
You don't need a CFA to show that four variables that are all affected by the same thing are highly correlated.
You might consider sending this to ida...@jiscmail.ac.uk (individual differences network), it's more focused on this sort of thing than the Lavaan list (which is about software).
Jeremy
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Abel Dean
Aug 7, 2023, 4:25:57 PM8/7/23
to lavaan
"'we are giants compared to people of 1800'. With that, you have proven yourself wrong. You asked for feedback and you got feedback.Maybe some kind of composite approach would be a better choice - Ibrahim"
And I thank you for that--our disagreement is beside the point. I will presume your full name is Ibrahim Nasser, and I will put you among the first in the acknowledgments, if not the first. Most of us are aware that people are much taller than within the 1800s, but we may not be aware how much taller. "Giants" may be hyperbole, but not by much.
Abel
Abel Dean
Aug 7, 2023, 4:34:14 PM8/7/23
to lavaan
"It's very clear why. It's wealth. Why is this useless?"
Wealth is certainly at the root of it, but it is not enough of an explanation, because there is no obvious link between having more money and getting a bigger skeleton. There is a link, yes, but we need to fill in the details.
"You don't need a CFA to show that four variables that are all affected by the same thing are highly correlated."
The problem is: that single thing is not GDP per capita. That single thing seems to be v-Loss. GDPpc would have a causal effect on v-Loss, and I have another structural equation model in that spirit, but I will omit it from my manuscript in future versions, as the SEM has an indirect feedback loop that may seem too dicey (spurious fitting) for reviewers.
"You might consider sending this to ida...@jiscmail.ac.uk (individual differences network), it's more focused on this sort of thing than the Lavaan list (which is about software)."
That's a great idea, I certainly will consult that network, thank you!
And, that is enough to put you, too, in the acknowledgments. I expect I will more fully explain in my manuscript why "wealth" is not enough of an explanation.
Abel
Ibrahim Nasser
Aug 7, 2023, 4:34:17 PM8/7/23
to lav...@googlegroups.com
You didn't even consider any data from 1800? Of course there could be a (causal) relationship between height and intelligence, apart from the obvious endogeneity problem. As Jeremy noted, this is probably not a lavaan issue.
Christian Arnold
Aug 7, 2023, 4:58:17 PM8/7/23
to lav...@googlegroups.com
Hi,
"Wealth is certainly at the root of it, but it is not enough of an explanation, because there is no obvious link between having more money and getting a bigger skeleton. There is a link, yes, but we need to fill in the details".
That may be true. There are probably intervening variables. But this does not invalidate Jeremy's statement. If you are interested in this, you should fit a mediation model.
I don't know the topic, however, I don't understand why QQ should explain vLoss. It seems like it's more or less the same thing. The phenomena do not discriminate each other. I also think that lavaan forum is not the right place for such topics.
HTH
Von: lav...@googlegroups.com <lav...@googlegroups.com> im Auftrag von Abel Dean <abel.d...@gmail.com>
Gesendet: Montag, August 7, 2023 10:42:37 PM
An: lavaan <lav...@googlegroups.com>
Betreff: Re: Poke holes in my grand-theory CFA
Gesendet: Montag, August 7, 2023 10:42:37 PM
An: lavaan <lav...@googlegroups.com>
Betreff: Re: Poke holes in my grand-theory CFA
To view this discussion on the web visit
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Abel Dean
Aug 7, 2023, 5:07:01 PM8/7/23
to lavaan
"Of course there could be a (causal) relationship between height and intelligence, apart from the obvious endogeneity problem."
If there is an overlooked causal path between height and intelligence (like smarter people eat better and therefore get taller, or something like that?), then I do not expect that would explain the unitary loading on v-Loss. But, I could be wrong, and I am happy to learn more.
"As Jeremy noted, this is probably not a lavaan issue."
Maybe, and I would count that as a step up, if it is really a matter of theory and not a matter of some elementary programming blunder. I will certainly go to that group Jeremy suggested.
Abel
"
Abel Dean
Aug 7, 2023, 5:19:51 PM8/7/23
to lavaan
Christian:
"That may be true. There are probably intervening variables. But this does not invalidate Jeremy's statement. If you are interested in this, you should fit a mediation model."
OK, I may learn more about mediation models, thanks!
"I don't know the topic, however, I don't understand why QQ should explain vLoss. It seems like it's more or less the same thing. The phenomena do not discriminate each other."
Yes, I claim that v-Loss is indeed the single factor explaining the shared variation, so QQ is no longer implicit, but the unitary loading means that QQ is v-Loss.
Abel
Keith Markus
Aug 8, 2023, 11:30:54 AM8/8/23
to lavaan
I am not a historian and I cannot provide a reference for this. However, my understanding is that mean height is specifically related to the amount of meat that people eat. People in the USA were shorter at the time of the Civil War due to less meat in their diets but at the time of the Revolutionary War the average height was about the same as it is today do to comparable meat consumption. The lower door frames during that period initially mislead historians but are now understood to reflect changing building practices rather than average height.
Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
Abel Dean
Aug 8, 2023, 12:00:57 PM8/8/23
to lavaan
Yes, that hypothesis is prominent within the field of physical anthropology, I examined it, and I think it follows from most people's intuitions. There is still no majority opinion, no "established" theory for the height trend within physical anthropology, nor for the many other secular trends within the respective fields. I collected a bunch of similar secular trends: greater height, greater intelligence, younger age at menarche, greater GDP per capita, greater longevity, older age at menopause, greater BMI, lesser child mortality, and lesser fertility. All of those trends match the directions of geographic covariance (from less advantaged to more advantaged countries). In my opinion, a likely explanation should explain all of those trends at the same time, if possible. The trend of increasing height, in particular, is especially curious, because adult height is 90% heritable. That means, at any given time, within any given society, the individual differences of adult height are 90% a matter of the genes (or the gene expressions) inherited from biological mothers and fathers. That should seem odd, because, within any given society, there is a diversity of people who eat a lot of meat or little meat or no meat. The very large heritability tells you that it tends to matter little what you do or what your parents do during your life--it is not going to affect your height so much. And yet people of northern European nations increased their height by 20 cm (7 inches) since the 19th century! It is a big puzzle, seemingly requiring a much different perspective than is typical. It is a puzzle seemingly overlooked by the physical anthropologists themselves, because they don't grant much relevance to heritability studies. Psychologists who specialize in intelligence (my background hobby) grant a lot of credit to heritability studies, and so they take the trend of increasing intelligence (the "Flynn effect") to be a puzzle of central focus (adult intelligence is 80% heritable). My theory is intended to solve all such puzzles at the same time.
Abel
Jeremy Miles
Aug 8, 2023, 1:44:07 PM8/8/23
to lav...@googlegroups.com
"The trend of increasing height, in particular, is especially curious, because adult height is 90% heritable. That means, at any given time, within any given society, the individual differences of adult height are 90% a matter of the genes"
No it doesn't. Imagine a very equal society, where people eat identically. Then the vast majority of the variance in height will be explained by genes.
Imagine another society where half the people are supplied with as much food as they want, and the other half is starved. Genes will account for a much smaller proportion of the variance.
Percentage of variance is a population parameter, and you cannot compare it across samples from different populations (like its analogy, reliability - it grinds my gears when authors write "This scale has been shown to be reliable."
J
Abel Dean
Aug 8, 2023, 1:58:15 PM8/8/23
to lav...@googlegroups.com
Yes, heritability depends as much upon environmental variation as it does upon genetic variation. But, it remains a puzzle why the height trend would have happened if it depended upon an environmental effect that is highly variant today, such as animal protein consumption (or medical care, or exercise, or toxins, and so on). If such things do not affect height so much today, then why should we think it made such a drastic difference across a hundred years? I think it is much easier to dismiss heritability studies (especially since confusions abound about the concept of heritability) than to recognize the actual puzzles. The puzzle if the height trend should be recognized as a very big puzzle in light of the very strong heritability, in my opinion.
Abel
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Abel Dean
Aug 13, 2023, 1:39:13 PM8/13/23
to lavaan
Hello again, lavaan aficionados.
Here is an update, thanks to a helpful member of this group. I used the method of discriminant validity, on a CFA model with two factors, one with only v-Loss and another with height, BMI and intelligence, to directly confirm that nearly no difference exists between those two factors.
I used the following code:
validitymodel <- '
QQ1 =~ vLoss
QQ2 =~ Height + Intelligence + BMI
Height ~~ BMI
'
validity.fit <- lavaan::cfa(validitymodel, data = MasSinDatSca, std.lv = TRUE)
print(semTools::discriminantValidity(validity.fit))
And here is the output:
lhs op rhs est ci.lower ci.upper Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
1 QQ1 ~~ QQ2 -0.987456 -1.029477 -0.945435 2 1312.625 1336.816 0.01780239 0 0 1 1
The 0.987 value is the same as the loading on v-Loss within the single-factor CFA.
I am only concerned that there may be too much overlap between those two methods. I would love to find a method that is more mathematically distinct to confirm the value approaching 1.0. Here is that code and lavaan output of the CFA with the single factor.
thismodel <- 'QuantityQuality =~
vLoss +
Height +
Intelligence +
BMI
Height ~~ BMI
'
thisfit <- lavaan::cfa(model = thismodel, estimator = "MLR", data = MasSinDatSca, meanstructure = T, order = F, auto.var = F)
summary(thisfit, rsquare = T, standardized = T, fit.measures = T)
Here is an update, thanks to a helpful member of this group. I used the method of discriminant validity, on a CFA model with two factors, one with only v-Loss and another with height, BMI and intelligence, to directly confirm that nearly no difference exists between those two factors.
I used the following code:
validitymodel <- '
QQ1 =~ vLoss
QQ2 =~ Height + Intelligence + BMI
Height ~~ BMI
'
validity.fit <- lavaan::cfa(validitymodel, data = MasSinDatSca, std.lv = TRUE)
print(semTools::discriminantValidity(validity.fit))
And here is the output:
lhs op rhs est ci.lower ci.upper Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
1 QQ1 ~~ QQ2 -0.987456 -1.029477 -0.945435 2 1312.625 1336.816 0.01780239 0 0 1 1
The 0.987 value is the same as the loading on v-Loss within the single-factor CFA.
I am only concerned that there may be too much overlap between those two methods. I would love to find a method that is more mathematically distinct to confirm the value approaching 1.0. Here is that code and lavaan output of the CFA with the single factor.
thismodel <- 'QuantityQuality =~
vLoss +
Height +
Intelligence +
BMI
Height ~~ BMI
'
thisfit <- lavaan::cfa(model = thismodel, estimator = "MLR", data = MasSinDatSca, meanstructure = T, order = F, auto.var = F)
summary(thisfit, rsquare = T, standardized = T, fit.measures = T)
Jošt Bartol
Aug 17, 2023, 4:30:40 AM8/17/23
to lav...@googlegroups.com
Hi, Abel,
Since you asked for (constructive) criticism, I will provide my two cents. I think that what your model is basically saying is:
1. QQ = v-Loss (std. factor loading = 0.99, basically these are the same thing).
2. Since std. factor loadings can be interpreted as correlations, you are simply correlating the QQ = v-Loss with height, intelligence and BMI (see the correlations in the supplied matrix, they are almost the same).
3. Given these, I do not see the value of the CFA. Why is it needed? I don't understand what the latent variable is here, and why it would be reflected in the four variables that you have. Maybe I am missing something, since I am not really familiar with the topic.
Sincerely,
Jošt
V V ned., 13. avg. 2023 ob 19:39 je oseba Abel Dean <abel.d...@gmail.com> napisala:
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Abel Dean
Aug 17, 2023, 8:55:46 AM8/17/23
to lav...@googlegroups.com
Jošt Bartol,
I am happy to explain.
I have two CFAs now.
The first CFA is represented by a latent variable "QuantityQuality" or "QQ" for the variation shared among all four indicator variables (v-Loss, intelligence, height, and BMI), and in that CFA I have a 0.99 loading on v-Loss. So, to answer your question, the latent variable is QuantityQuality or QQ.
Without CFA, I don't think I can get those latent variables.
Abel
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Keith Markus
Aug 23, 2023, 8:08:48 AM8/23/23
to lavaan
This is an attempt to recreate something that I attempted to post several days ago. I am not sure what I did but it showed as posted at my end but was apparently never distributed and when I sign in now I see "Message has been deleted" at the bottom of the list and no longer see my attempted post. Like Ian
Anderson when he had to remix half of Thick as a Brick, I cannot help but think that it came out better on the first try. :-) But here goes...
Jost and Abel, I read your exchange with interest and here are some further thoughts. It seems to me that the test Abel describes tests whether more than one latent variable is needed but does not test what I take Jost to be suggesting which is that less than one may be needed.
If the statistical relationship is that v-loss accounts for the shared variance between the other three variables, then another way to model that is with a path model in which v-loss is the common cause of the other three variables (height, intelligence, BMI). Abel, if you embrace that model, then it is more parsimonious than the model with the latent variable. If you reject the model, then it poses a plausible rival hypothesis from which you want to distinguish your model. Perhaps you can obtain data from some other context in which QQ and v-loss are not so highly correlated for this purpose.
Finally, conditional independence is a statistical phenomenon, a hopefully reproducible pattern in the joint probability distribution of the variables. However, in itself it is not an explanation, it is instead what needs explaining. In order for the CFA model to provide an explanation and not just a descriptive summary, it seems to me that we need a detailed account of what kind of property of country-times (the unit of analysis) QQ is. We also need an account of how QQ as an independent property causes the four observed variables. By this, I do not mean mediating variables, that would lead to an infinite regress. What I mean is an explanatory account of the process or mechanisms in the world by which the QQ property is able to influence the other four variables.
This is not my substantive area of expertise. I hope these comments are helpful.
Abel Dean
Aug 23, 2023, 9:51:56 AM8/23/23
to lavaan
Dear Keith A. Markus,
Thank you so much for all of your critical attention and advice. I will gladly put your name, too, in the acknowledgments.
"If the statistical relationship is that v-loss accounts for the shared variance between the other three variables, then another way to model that is with a path model in which v-loss is the common cause of the other three variables (height, intelligence, BMI)."
Funny you mention it, because in fact I do have a well-fitting structural equation model (SEM) that omits the latent QQ, includes GDP per capita, and may be a better representation of the actual causal network. The respective path diagram is below.
Before, I took it to be a clarification of the CFA. But, I put it away after Rex Kline pointed out that the indirect feedback loop with no instrumental variables and with no correlated errors (like reciprocal causes or common causes) for all three pairs of variables in the loop may seem unlikely to readers, too much to presume, and I have no way of solving that problem. But, maybe I can still present it as something possible.
"Perhaps you can obtain data from some other context in which QQ and v-loss are not so highly correlated for this purpose."
Yes, but I would like to save that for my next project. I will preregister and try to validate the unitary loading within the CFA on an independent data set; I am thinking I will use maybe USA county-level data.
"Finally, conditional independence is a statistical phenomenon, a hopefully reproducible pattern in the joint probability distribution of the variables. However, in itself it is not an explanation, it is instead what needs explaining. In order for the CFA model to provide an explanation and not just a descriptive summary, it seems to me that we need a detailed account of what kind of property of country-times (the unit of analysis) QQ is. We also need an account of how QQ as an independent property causes the four observed variables. By this, I do not mean mediating variables, that would lead to an infinite regress. What I mean is an explanatory account of the process or mechanisms in the world by which the QQ property is able to influence the other four variables."
Yes, I agree. I am claiming that QQ is equivalent to v-Loss, and so it would help to have a strong mechanistic argument to reinforce the causal link between v-Loss and the variation common to height, BMI, and intelligence. That is in the "Theory" part of my manuscript, but I expect I need more, maybe examples in non-human species in which a shift toward quality on the quantity-quality spectrum produces greater body size, adiposity and intelligence. In Discussion I have an comparison to the transition from grasshoppers to locusts (locust phase polyphenism), which is likewise a shift from offspring quantity to offspring quality, it captures all three plastic trait shifts, and I may move that section to Theory. It is a lot of theory but may not be as solid as we would like, as the molecular genetic and epigenetic mechanisms are still largely a black box.
"This is not my substantive area of expertise. I hope these comments are helpful."
Yes, your comments are most certainly helpful, and don't worry, because it is NOBODY'S substantive area of expertise.
Thank you so much for all of your critical attention and advice. I will gladly put your name, too, in the acknowledgments.
"If the statistical relationship is that v-loss accounts for the shared variance between the other three variables, then another way to model that is with a path model in which v-loss is the common cause of the other three variables (height, intelligence, BMI)."
Before, I took it to be a clarification of the CFA. But, I put it away after Rex Kline pointed out that the indirect feedback loop with no instrumental variables and with no correlated errors (like reciprocal causes or common causes) for all three pairs of variables in the loop may seem unlikely to readers, too much to presume, and I have no way of solving that problem. But, maybe I can still present it as something possible.
"Perhaps you can obtain data from some other context in which QQ and v-loss are not so highly correlated for this purpose."
"Finally, conditional independence is a statistical phenomenon, a hopefully reproducible pattern in the joint probability distribution of the variables. However, in itself it is not an explanation, it is instead what needs explaining. In order for the CFA model to provide an explanation and not just a descriptive summary, it seems to me that we need a detailed account of what kind of property of country-times (the unit of analysis) QQ is. We also need an account of how QQ as an independent property causes the four observed variables. By this, I do not mean mediating variables, that would lead to an infinite regress. What I mean is an explanatory account of the process or mechanisms in the world by which the QQ property is able to influence the other four variables."
"This is not my substantive area of expertise. I hope these comments are helpful."
Abel
Jošt Bartol
Aug 25, 2023, 3:26:00 AM8/25/23
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Keith and Abel,
I am sorry for my late reply, I got caught in something and completely forgot about this ...
Anyway, Abel, in my previous post I am actually saying exactly what Keith is saying ("
we need a detailed account of what kind of property of country-times
(the unit of analysis) QQ is. We also need an account of how QQ as an
independent property causes the four observed variables.").
If I correctly understand what you are trying to say is that there is something called QQ, and this QQ is some property that each country has. The variation in this QQ explains mortality, BMI, intelligence, and height. However, what is absent from your posts is what QQ actually is. Theoretically defining QQ is key because otherwise QQ can be anything. Relatedly, I am also interested why exactly these four indicators (v-Loss, BMI, IQ, height) and no others are included. Since you are (I assume) considering QQ as a reflective construct, you could also consider other indicators that reflect QQ.
Now, if QQ is v-loss (or mortality; which your model shows and you also say yourself, "I am claiming that QQ is equivalent to v-Loss"), then why do we need QQ? Why cannot we just explain the variability among the variables without QQ? With, as Keith suggested, path analysis, or some other method, that is intended to assess variance among variables. This is a crucial point that is lacking in your thesis.
To summarize, it would be very helpful if you provided a theoretical account of what QQ is and how it is reflected in the countries' (average?) v-Loss, BMI, IQ, and height.
Best,
Jošt
V V sre., 23. avg. 2023 ob 15:52 je oseba Abel Dean <abel.d...@gmail.com> napisala:
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Abel Dean
Aug 25, 2023, 5:28:59 PM8/25/23
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Dear Jošt Bartol,
I am happy you are giving me guidance, because it has been helpful. You are acknowledged.
The latent variable QQ may be unnecessary. If I had another way of showing that the shared variance among height, BMI and intelligence is equal to v-Loss, then I wouldn't need QQ. But, I don't know of another way.
On the other hand, QQ represents the offspring quantity-quality trade-off of life-history theory, which goes to the underlying theory and aids understanding the evolutionary mechanism: human genes are expressing themselves either in favor of MANY children or in favor of BETTER children. When there is high juvenile mortality (v-Loss), our genes go for many children, and otherwise our genes go for better children.
An interesting comparison that may help understand the concept is the biological shift from grasshoppers to locusts. Here is the respective excerpt from my manuscript:
A method of understanding nearly any pattern of human biology is to look outside the human species to find a similar pattern, and, in this case, an informative parallel is the shift between solitarius grasshoppers and gregarious locusts (locust phase polyphenism). The comparison is far from perfect, as the evolutionary relationship is distant and the many differences of the comparison compete with the many similarities, but nevertheless the similarities serve as relevant biological background knowledge to aid understanding of the hypothesis of this paper. Solitarious grasshoppers and the respective gregarious locusts are the same genotype (same species and race), but they are two different states along a spectrum of life-history strategy. Solitarious grasshoppers are at the end of the spectrum with the strategy of offspring quantity, whereas gregarious locusts prefer offspring quality (Uvarov, 1961). Readers may have expected that locusts, composed of swarms with billions, would instead prefer the strategy of quantity, but locusts have a lesser total fertility rate than the respective grasshoppers (Pener, 1991), and so the fast population growth is achieved through faster individual development and greater survival (Pener & Simpson, 2009; Uvarov, 1966). For Locusta migratoria, relative to their solitarious counterparts, the survival and reproduction of gregarious locusts are aided by bigger bodies of hatchlings, bigger bodies of adult males, faster female sexual maturation, longer lives (Pener & Simpson, 2009; Uvarov, 1966) and wider heads (Tanaka & Zhu, 2005). Wider heads likely accommodate, according to a study of Schistocerca gregaria, larger brains (Ott & Rogers, 2010). The analogy with the human species falls short mainly upon considering that the cue for the grasshopper-to-locust shift is population density, not v-Loss.
So, many traits of grasshoppers/locusts are related to this environmental cue of population density, and otherwise the only thing they have in common is the abstract construct of "quantity-quality." Grasshoppers each reproduce a large number of baby grasshoppers, whereas locusts reproduce fewer but better baby locusts. Grasshoppers are about quantity, whereas locusts are about quality. Similarly, I claim that humans over the last hundred years have shifted from quantity to quality.
I expect that is clearer, but I expect more direct evidence would be better. I have only the big-picture stuff, none of the biochemical mechanisms or whatever. It is that way with grasshoppers and locusts, too. Let me know what you think, one way or the other.
"Relatedly, I am also interested [in] why exactly these four indicators (v-Loss, BMI, IQ, height) and no others are included."
That would be just because those four variables are the only four variables in which I have a large number of countries at a single cross section in time (1995). But, I may add another variable soon: growth speed. I discovered that the NCD Collaboration Project in 2020 released global longitudinal country-level height data for age classes between 5 and 19, so it occured to me yesterday that it means I can calculate growth rates (a variable of quality, as with grasshoppers and locusts), like maybe the age at peak height velocity. I am still working on it. Before, I had only age at menarche to represent developmental speed, which is unreliable data for few countries not organized by time, so I could not include it in my factor analyses.
Abel
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Keith Markus
Aug 26, 2023, 8:36:55 AM8/26/23
to lavaan
Abel,
I am not clear why you wrote this:
>>>
The latent variable QQ may be unnecessary. If I had another way of
showing that the shared variance among height, BMI and intelligence is
equal to v-Loss, then I wouldn't need QQ. But, I don't know of another
way.
>>>
The common cause path model tests whether v-loss can fully account for the association between the other three variables.
It occurs to me that you also have two rival interpretations of your latent variable model to contend with. You can interpret it as a reflective measurement model for QQ. However, a second interpretation is that v-loss is a single indicator of QQ and the other three parameters interpreted as loadings in the CFA interpretation are instead here interpreted as effects of a common cause. This changes the interpretation of QQ in a way that Jost's suggestion to seek further indictors would directly address. These are what I describe as syntactically equivalent models. They will always provide the same fit because they are identical in syntax, but they provide rival hypotheses regarding the interpretation of that data. The only way to empirically distinguish them is to strategically add variables to the model that cause the two interpretations to diverge in syntax.
Markus, K. A. (2008). Hypothesis formulation, model
interpretation, and model equivalence: Implications of a
mereological causal interpretation of structural equation
models. Multivariate
Behavioral Research, 43, 177-209.
A more general discussion of the benefits to causal inference from including additional variables, including variables for which no causal effect is predicted, can be found in Robert Abelson's book where he describes a specific pattern of effects as a "signature". I understand that data may be limited but it is still important to consider how these issues impact your inferences even if you cannot immediately add more variables.
Abelson, R. A. (2012). Statistics as principled argument. New York: Taylor and Francis. (originally published 1995)
Finally, if you are not already aware of it, you might be interested in the below very interesting chapter on causation in biology.
McLaughlin, P. (2007). On selection of, for, with and against. In P. Machamer and G. Wolters (Eds.), Thinking about causation: From Greek philosophy to modern physics (pp. 265-283). Pittsburgh, PA: University of Pittsburgh.
I hope that helps,
Abel Dean
Aug 26, 2023, 5:16:33 PM8/26/23
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Dear Dr. Keith Markus,
Thank you for your attention to this problem. You suggested,
"The common cause path model tests whether v-loss can fully account for the association between the other three variables."
Yes, but such a model does not seem to indicate whether or not v-Loss accounts for 100% of the variation shared by intelligence, height, and BMI (except for the error covariance). Maybe you had something else in mind, but, to illustrate what I did today, here is my code for an SEM, cutting out the "QQ" middleman and depending on vLoss as the causal variable:
mysemmodel <- 'BMI ~ vLossIntelligence ~ vLossHeight ~ vLossIntelligence ~~ 0*HeightBMI ~~ HeightIntelligence ~~ 0*BMI'mysemfit <- lavaan::sem(model = mysemmodel, data = PriSinDatSca, meanstructure = F, estimator = "MLR", order = F, auto.var = F)
The results are well fitting, but I don't see a 0.99 loading or 0.98 R^2 or anything like that:
> print(mysemsummary)
lavaan 0.6.16 ended normally after 10 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 7
Used Total
Number of observations 152 224
Model Test User Model:
Standard Scaled
Test Statistic 0.351 0.403
Degrees of freedom 2 2
P-value (Chi-square) 0.839 0.818
Scaling correction factor 0.871
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 401.364 273.741
Degrees of freedom 6 6
P-value 0.000 0.000
Scaling correction factor 1.466
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.013 1.018
Robust Comparative Fit Index (CFI) 1.000
Robust Tucker-Lewis Index (TLI) 1.011
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -436.731 -436.731
Scaling correction factor 1.314
for the MLR correction
Loglikelihood unrestricted model (H1) -436.555 -436.555
Scaling correction factor 1.215
for the MLR correction
Akaike (AIC) 887.462 887.462
Bayesian (BIC) 908.629 908.629
Sample-size adjusted Bayesian (SABIC) 886.474 886.474
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.092 0.110
P-value H_0: RMSEA <= 0.050 0.886 0.842
P-value H_0: RMSEA >= 0.080 0.066 0.098
Robust RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.091
P-value H_0: Robust RMSEA <= 0.050 0.877
P-value H_0: Robust RMSEA >= 0.080 0.066
Standardized Root Mean Square Residual:
SRMR 0.007 0.007
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
BMI ~
vLoss -0.654 0.042 -15.574 0.000 -0.654 -0.690
Intelligence ~
vLoss -0.761 0.049 -15.381 0.000 -0.761 -0.747
Height ~
vLoss -0.861 0.047 -18.210 0.000 -0.861 -0.826
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intelligence ~~
.Height 0.000 0.000 0.000
.BMI ~~
.Height 0.066 0.039 1.678 0.093 0.066 0.172
.Intelligence 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.BMI 0.448 0.072 6.188 0.000 0.448 0.524
.Intelligence 0.438 0.078 5.646 0.000 0.438 0.442
.Height 0.330 0.037 9.001 0.000 0.330 0.318
R-Square:
Estimate
BMI 0.476
Intelligence 0.558
Height 0.682
But, maybe what I am looking for is in the "parameterEstimates" function. Line #10 says "vLoss ~~ vLoss 0.954", but I am not sure what that means. You know lavaan better than me, so maybe you know if it is what I am looking for.
Pe <- lavaan::parameterEstimates(mysemfit, rsquare = T, standardized = T)print(Pe)
> print(Pe)
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all std.nox
1 BMI ~ vLoss -0.654 0.042 -15.574 0.000 -0.736 -0.571 -0.654 -0.690 -0.707
2 Intelligence ~ vLoss -0.761 0.049 -15.381 0.000 -0.858 -0.664 -0.761 -0.747 -0.765
3 Height ~ vLoss -0.861 0.047 -18.210 0.000 -0.954 -0.769 -0.861 -0.826 -0.846
4 Intelligence ~~ Height 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
5 BMI ~~ Height 0.066 0.039 1.678 0.093 -0.011 0.143 0.066 0.172 0.172
6 BMI ~~ Intelligence 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
7 BMI ~~ BMI 0.448 0.072 6.188 0.000 0.306 0.590 0.448 0.524 0.524
8 Intelligence ~~ Intelligence 0.438 0.078 5.646 0.000 0.286 0.590 0.438 0.442 0.442
9 Height ~~ Height 0.330 0.037 9.001 0.000 0.258 0.402 0.330 0.318 0.318
10 vLoss ~~ vLoss 0.954 0.000 NA NA 0.954 0.954 0.954 1.000 0.954
11 BMI r2 BMI 0.476 NA NA NA NA NA NA NA NA
12 Intelligence r2 Intelligence 0.558 NA NA NA NA NA NA NA NA
13 Height r2 Height 0.682 NA NA NA NA NA NA NA NAI know you made other great points, and I am not ignoring them, but for now let's focus on this one. Thanks!
Yours,
Mr. Abel Dean
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Keith Markus
Aug 27, 2023, 8:19:53 AM8/27/23
to lavaan
Abel,
Google Groups appears to delete internet quotation marks, I had marked of the quoted text in what I posted but it does not appear that way.
If you fit the model with no covariances between disturbances of the three endogenous variables, then the chi-square goodness of fit test tests the hypothesis that the exogenous variable (v-Loss) accounts for all the covariation between the endogenous variables (BMI, Height and Intelligence). If you reject the fit of the model, and the ill fit is not traceable to some other aspect of the model, then the hypothesis is not supported. It appears that you freed one covariance in the model that you fit.
If you then free all three covariances and conduct a chi-square difference test with the model with fixed zero covariances (same as omitted), then this provides an ombibus test of the hypothesis that all three covariances are zero. If you reject the constraints, then the hypothesis that the covariances are not needed is not supported.
The covariances between the endogenous variables are essentially partitioned between what is explained by the exogenous variable and the covariances between the disturbances. So, if the covariances between disturbances are zero, then everything is explained by the exogenous variable. You can also look at the confidence intervals around the covariances between disturbances in the model in which these are free to get a sense of how large they might be within sampling error.
I have never seen this done before but if you really want a numeric index, I imagine that you could create a defined parameter as the sum of the three covariances, or sum of squares if the signs are not the same, and look at a confidence interval for that too see how far it gets from zero.
Keith,
Abel Dean
Aug 28, 2023, 1:35:38 PM8/28/23
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Dear Dr. Keith A. Markus,
Thank you for your continued attention and guidance. I took away the error covariance, and as you can see the results (shown below) are worse but still very good.
I will send another email to you privately.
Yours,
Mr. Abel Dean
SEM summary:
lavaan 0.6.16 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 6
Used Total
Number of observations 152 224
Model Test User Model:
Standard Scaled
Test Statistic 4.889 4.490
Degrees of freedom 3 3
P-value (Chi-square) 0.180 0.213
Scaling correction factor 1.089
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 401.364 273.741
Degrees of freedom 6 6
P-value 0.000 0.000
Scaling correction factor 1.466
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.995 0.994
Tucker-Lewis Index (TLI) 0.990 0.989
Robust Comparative Fit Index (CFI) 0.996
Robust Tucker-Lewis Index (TLI) 0.992
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -439.000 -439.000
Scaling correction factor 1.278
for the MLR correction
Loglikelihood unrestricted model (H1) -436.555 -436.555
Scaling correction factor 1.215
for the MLR correction
Akaike (AIC) 890.000 890.000
Bayesian (BIC) 908.143 908.143
Sample-size adjusted Bayesian (SABIC) 889.153 889.153
Root Mean Square Error of Approximation:
RMSEA 0.064 0.057
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.163 0.154
P-value H_0: RMSEA <= 0.050 0.320 0.362
P-value H_0: RMSEA >= 0.080 0.487 0.434
Robust RMSEA 0.060
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.165
P-value H_0: Robust RMSEA <= 0.050 0.349
P-value H_0: Robust RMSEA >= 0.080 0.468
Standardized Root Mean Square Residual:
SRMR 0.023 0.023
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
BMI ~
vLoss -0.654 0.042 -15.574 0.000 -0.654 -0.690
Intelligence ~
vLoss -0.761 0.049 -15.381 0.000 -0.761 -0.747
Height ~
vLoss -0.861 0.047 -18.210 0.000 -0.861 -0.826
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intelligence ~~
.Height 0.000 0.000 0.000
.BMI ~~
.Height 0.000 0.000 0.000
.Intelligence 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.BMI 0.448 0.072 6.188 0.000 0.448 0.524
.Intelligence 0.438 0.078 5.646 0.000 0.438 0.442
.Height 0.330 0.037 9.001 0.000 0.330 0.318
R-Square:
Estimate
BMI 0.476
Intelligence 0.558
Height 0.682
BMI Intllg Height vLoss
BMI 0.000
Intelligence 0.017 0.000
Height 0.070 0.014 0.000
vLoss 0.000 0.000 0.000 0.000
SEM fit indices:
npar fmin chisq
6.000 0.016 4.889
df pvalue chisq.scaled
3.000 0.180 4.490
df.scaled pvalue.scaled chisq.scaling.factor
3.000 0.213 1.089
baseline.chisq baseline.df baseline.pvalue
401.364 6.000 0.000
baseline.chisq.scaled baseline.df.scaled baseline.pvalue.scaled
273.741 6.000 0.000
baseline.chisq.scaling.factor cfi tli
1.466 0.995 0.990
cfi.scaled tli.scaled cfi.robust
0.994 0.989 0.996
tli.robust nnfi rfi
0.992 0.990 0.976
nfi pnfi ifi
0.988 0.494 0.995
rni nnfi.scaled rfi.scaled
0.995 0.989 0.967
nfi.scaled pnfi.scaled ifi.scaled
0.984 0.492 0.994
rni.scaled nnfi.robust rni.robust
0.994 0.992 0.996
logl unrestricted.logl aic
-439.000 -436.555 890.000
bic ntotal bic2
908.143 152.000 889.153
scaling.factor.h1 scaling.factor.h0 rmsea
1.215 1.278 0.064
rmsea.ci.lower rmsea.ci.upper rmsea.ci.level
0.000 0.163 0.900
rmsea.pvalue rmsea.close.h0 rmsea.notclose.pvalue
0.320 0.050 0.487
rmsea.notclose.h0 rmsea.scaled rmsea.ci.lower.scaled
0.080 0.057 0.000
rmsea.ci.upper.scaled rmsea.pvalue.scaled rmsea.notclose.pvalue.scaled
0.154 0.362 0.434
rmsea.robust rmsea.ci.lower.robust rmsea.ci.upper.robust
0.060 0.000 0.165
rmsea.pvalue.robust rmsea.notclose.pvalue.robust rmr
0.349 0.468 0.022
rmr_nomean srmr srmr_bentler
0.022 0.023 0.023
srmr_bentler_nomean crmr crmr_nomean
0.023 0.030 0.030
srmr_mplus srmr_mplus_nomean cn_05
0.023 0.023 243.968
cn_01 gfi agfi
353.724 0.997 0.989
pgfi mfi ecvi
0.299 0.994 0.111
SEM parameter estimates:
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all std.nox
1 BMI ~ vLoss -0.654 0.042 -15.574 0 -0.736 -0.571 -0.654 -0.690 -0.707
2 Intelligence ~ vLoss -0.761 0.049 -15.381 0 -0.858 -0.664 -0.761 -0.747 -0.765
3 Height ~ vLoss -0.861 0.047 -18.210 0 -0.954 -0.769 -0.861 -0.826 -0.846
4 Intelligence ~~ Height 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
5 BMI ~~ Height 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
6 BMI ~~ Intelligence 0.000 0.000 NA NA 0.000 0.000 0.000 0.000 0.000
7 BMI ~~ BMI 0.448 0.072 6.188 0 0.306 0.590 0.448 0.524 0.524
8 Intelligence ~~ Intelligence 0.438 0.078 5.646 0 0.286 0.590 0.438 0.442 0.442
9 Height ~~ Height 0.330 0.037 9.001 0 0.258 0.402 0.330 0.318 0.318
10 vLoss ~~ vLoss 0.954 0.000 NA NA 0.954 0.954 0.954 1.000 0.954
11 BMI r2 BMI 0.476 NA NA NA NA NA NA NA NA
12 Intelligence r2 Intelligence 0.558 NA NA NA NA NA NA NA NA
13 Height r2 Height 0.682 NA NA NA NA NA NA NA NA
lhs op rhs est.std se z pvalue ci.lower ci.upper
1 BMI ~ vLoss -0.690 0.039 -17.823 0 -0.766 -0.614
2 Intelligence ~ vLoss -0.747 0.042 -17.766 0 -0.829 -0.665
3 Height ~ vLoss -0.826 0.021 -38.555 0 -0.868 -0.784
4 Intelligence ~~ Height 0.000 0.000 NA NA 0.000 0.000
5 BMI ~~ Height 0.000 0.000 NA NA 0.000 0.000
6 BMI ~~ Intelligence 0.000 0.000 NA NA 0.000 0.000
7 BMI ~~ BMI 0.524 0.053 9.806 0 0.419 0.629
8 Intelligence ~~ Intelligence 0.442 0.063 7.037 0 0.319 0.565
9 Height ~~ Height 0.318 0.035 8.991 0 0.249 0.387
10 vLoss ~~ vLoss 1.000 0.000 NA NA 1.000 1.000
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Jošt Bartol
Aug 29, 2023, 10:37:15 AM8/29/23
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Hi Abel Dean,
Thanks for the clarification. I understand better what you are trying to do and show. I think that the last model better communicates that idea than the original model with the latent QQ (as noted, I, and probably many others, would assume that you are proposing a measurement model of QQ). I also think suggestions by Keith are very helpful, especially how to model your hypothesis.
Still, I have just two notes.
The first is very technical. In one of your previous comments you said "
whether or not v-Loss accounts for 100% of the variation shared by intelligence, height, and BMI (except for the error covariance).
" You couldn't test this either with CFA. In fact, the R-squares there and in the last analysis are probably very close.
The second is a bit more theoretical, but relates directly to the statistical model. As long as you were proposing QQ as a latent variable or simply trying to understand the variance among the four variables, this didn't seem like an issue. However, when I looked at the final model, it strikes me that you are now hypothesizing that v-Loss (i.e., the level of juvenile mortality in a country, if I understand correctly) predicts or even causes BMI, intelligence, and height. I find this striking because didn't we (humans) decrease (juvenile) mortality exactly by becoming smarter and being able to grow more food? In other words, the shift from quantity to quality might not be genetic, but social. As we as humans become more free and unbound by gratifying our material needs, we can focus on 'higher order' needs, such as self-realization. In the same manner, we want kids who grow up to be strong and independent, and self-realizing, even if this means having fewer children. Maybe you already thought about that, but I am still curious.
Best,
Jošt
V V pon., 28. avg. 2023 ob 19:35 je oseba Abel Dean <abel.d...@gmail.com> napisala:
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Abel Dean
Aug 29, 2023, 11:28:15 AM8/29/23
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Jošt, you wrote,
"Thanks for the clarification. I understand better what you are trying to do and show. I think that the last model better communicates that idea than the original model with the latent QQ (as noted, I, and probably many others, would assume that you are proposing a measurement model of QQ). I also think suggestions by Keith are very helpful, especially how to model your hypothesis."
Yes, I like that model, because it more directly reflects my hypothesis of the causal relationships: I am claiming that lesser v-Loss causes greater height, intelligence and BMI. I am still not completely sure that the fit statistics prove the point that v-Loss accounts for ALL the shared variance, but Dr. Markus claims something like that, so I will need to figure out why.
"In one of your previous comments you said ' whether or not v-Loss accounts for 100% of the variation shared by intelligence, height, and BMI (except for the error covariance). ' You couldn't test this either with CFA. In fact, the R-squares there and in the last analysis are probably very close."
The trouble with interpreting such a thing from the R-squares is that I am not claiming that v-Loss accounts for all the variation, but only all of the shared variation. For any one of those three traits, v-Loss does not explain everything, but v-Loss seems to be the common factor for all three together.
"The second is a bit more theoretical, but relates directly to the statistical model. As long as you were proposing QQ as a latent variable or simply trying to understand the variance among the four variables, this didn't seem like an issue. However, when I looked at the final model, it strikes me that you are now hypothesizing that v-Loss (i.e., the level of juvenile mortality in a country, if I understand correctly) predicts or even causes BMI, intelligence, and height. I find this striking because didn't we (humans) decrease (juvenile) mortality exactly by becoming smarter and being able to grow more food? In other words, the shift from quantity to quality might not be genetic, but social. As we as humans become more free and unbound by gratifying our material needs, we can focus on 'higher order' needs, such as self-realization. In the same manner, we want kids who grow up to be strong and independent, and self-realizing, even if this means having fewer children. Maybe you already thought about that, but I am still curious."
I am happy to explain. My perspective is much more biological than is typical in the social sciences, and so I am looking at the quantitative human patterns and making sense of it all as though the human species is just another species of primates.
I invite you to interview people you know with the following question: "In which of these two types of environment would you prefer to be a parent to a greater number of children: (1) safer environments or (2) more-dangerous environments?"
It would be a plausible prediction that ABSOLUTELY EVERYONE you talk to would answer, "safer environments." If our reproductive habits were really guided by such interests of the upper brain, then this would be the global pattern: we would reproduce more in safer environments. And yet our actual reproductive habits are directly the opposite; the most dangerous environments are also the most reproductive settings, i.e. South Sudan during famine and war was the place with the highest total fertility rate. There is a nearly unitary relationship between v-Loss and crude birth rate (but I omitted it from my models because it is a reciprocal relationship).
There is nothing more biological than reproduction, and our seat of reproductive decisions almost certainly did not migrate to a different part of the brain when our ancestors evolved larger brains. Such a pattern of reproductive decisions--reproducing when it is LEAST safe--made sense for the genomes of our primate/mammal ancestors, because it is not about being interested in the welfare of babies, but it is about the persisting survival of genes. Such genes can be invested in either many babies each with low survival probability or into a few babies each with high survival probability.
This perspective should be intuitively obvious, in my opinion, but it is a perspective largely foreign to social scientists at large. Talk to demographers and economists who model the demographic transitions, for example, and, yes, they will talk about a quantity-quality trade-off, but they think it is all about rational choices, the same way you would buy dishes. If your dishes are likely to break, then you would rather buy many cheap dishes then a few high-quality dishes, and they think that is similar to the way we have children. Evolutionary biology be damned.
Thanks for the question, because I love talking about this stuff.
Abel
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Keith Markus
Aug 30, 2023, 9:24:17 AM8/30/23
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Abel,
Sorry if I was not clear. According to the path model with only the three effects of vloss on the other three variables and the residual variances (no residual covariances), the only source of covariation between the other three variables is vloss. Normally this is an unanticipated implication of a model that I find myself warning researchers about. In your case, it is intentional. According to the model, the remaining three variables are statistically independent conditional on vloss.
Keith
Abel Dean
Aug 30, 2023, 9:29:31 AM8/30/23
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Dr. Markus,
Thank you, I think that makes sense. I may make it another argument for my paper, to reinforce the inference from the unitary loading within the CFA.
Yours,
Abel
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Jošt Bartol
Sep 4, 2023, 2:26:28 AM9/4/23
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Abel,
thanks for the clarification. I will admit, it makes sense, even though I do not really agree with it (as I am a social scientist).
To be fair, you also said that economists etc. say the same thing as you "they think it is all about rational choices, the same way you would buy
dishes. If your dishes are likely to break, then you would rather buy
many cheap dishes then a few high-quality dishes, and they think that is
similar to the way we have children." I think this is reasonable and it also makes sense in light of safer/more dangerous environments (and would explain the 'paradoxical behavior' that you suggested with the hypothetical question). In other words, a joint look on these issues may be beneficial. But, I am not a demographer or evolutionary biologist, so I will leave it at that.
Good luck!
Jošt
V V sre., 30. avg. 2023 ob 15:29 je oseba Abel Dean <abel.d...@gmail.com> napisala:
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Abel Dean
Sep 4, 2023, 1:14:17 PM9/4/23
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Jošt,
Right, the analogy of the dishes works correctly, in my opinion, except it is the way our genes behave, not the behavioral mechanism of our economical purchasing decisions of kitchen goods. We prefer to reproduce more in dangerous environments, and we have no conscious idea of why we do that. Within my perspective (and I generally recommend this perspective): EVERYTHING about the human species is biology. If an objective phenomenon of the human species is not biology, then biology needs to be adjusted to accommodate that phenomenon. The way social scientists tend to behave is that they bring in biology only if they must. But I suggest the opposite: look outside biology only if you must. You heard of the slur, "biological determinism." What if we studied earthquakes, and, upon hearing any explanation grounded in standard geological models such as tectonic plates, we responded, "Oh, I would rather avoid geological determinism"? Of course that would be ridiculous, and social scientists behave similarly with explanations for the human species, therefore failing to make proper sense of the human species, allowing autodidacts like me to fill in that knowledge vacuum. That is great for me, but it is tragic for the social sciences, and it withholds from the whole human community the benefits of scientific progress. You are a professional social scientist, so I suggest taking the necessary leap and breaking that spell.
Yours,
Abel
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Abel Dean
Sep 29, 2023, 9:49:30 AM9/29/23
to lavaan
Update: I revised my manuscript and I carried out much of the guidance I received in this group (got a simple SEM that is just a small adjustment of the preferred CFA and reinforces the inference), so thank you Dr. Keith Markus and everyone else. I rewrote the manuscript for a target audience of intelligence researchers, and I submitted it last night to Journal of Intelligence. Here is a link to that preprint.
https://figshare.com/articles/preprint/How_to_explain_human_differences_across_time_geography_and_disciplines/23623698
Abel Dean
https://figshare.com/articles/preprint/How_to_explain_human_differences_across_time_geography_and_disciplines/23623698
Abel Dean
Christian Arnold
Sep 29, 2023, 10:50:39 AM9/29/23
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Congrats, Abel!
From: lav...@googlegroups.com <lav...@googlegroups.com> on behalf of Jošt Bartol <barto...@gmail.com>
Sent: Monday, September 4, 2023 8:25:58 AM
To: lav...@googlegroups.com <lav...@googlegroups.com>
Subject: Re: Poke holes in my grand-theory CFA
Sent: Monday, September 4, 2023 8:25:58 AM
To: lav...@googlegroups.com <lav...@googlegroups.com>
Subject: Re: Poke holes in my grand-theory CFA
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