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Aryanne van Delft
Aug 3, 2018, 5:49:34 AM8/3/18
to lavaan
Hi everyone,
I have a question. My model shows negative covariances for the observed variables but I do not understand why
WSPISNPBCATTINTHAG <- '
# Latent variables
Intention =~ 1*I2 + A8 + A14
Hagerbaum =~ 1*H1 + H2 + H3 + H4 + H5 + H6
Attitude =~ 1*A1 + A5 + A6
PerceivedBehavioralControl =~ 1*A3 + A10
# Regression
Hagerbaum ~ Intention + PerceivedBehavioralControl
Intention ~ Attitude + PerceivedBehavioralControl + A9 + SS + JD + WJI + WTC
'
# Run Lavaan
MODELWSPISNPBCATTINTHAG <- sem(model = WSPISNPBCATTINTHAG, data=mydata, orthogonal=FALSE, std.lv=TRUE)
summary(MODELWSPISNPBCATTINTHAG, fit.measures=TRUE, standardized=TRUE)
#covariantiematrix
lavInspect(MODELWSPISNPBCATTINTHAG, "h1")
inspect(MODELWSPISNPBCATTINTHAG,"cor.all",)
inspect(MODELWSPISNPBCATTINTHAG, "rsquare")
lavaan (0.6-1) converged normally after 36 iterations
Number of observations 219
Estimator ML
Model Fit Test Statistic 260.131
Degrees of freedom 141
P-value (Chi-square) 0.000
Model test baseline model:
Minimum Function Test Statistic 1607.013
Degrees of freedom 161
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.918
Tucker-Lewis Index (TLI) 0.906
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5092.353
Loglikelihood unrestricted model (H1) -4962.288
Number of free parameters 34
Akaike (AIC) 10252.706
Bayesian (BIC) 10367.935
Sample-size adjusted Bayesian (BIC) 10260.190
Root Mean Square Error of Approximation:
RMSEA 0.062
90 Percent Confidence Interval 0.050 0.074
P-value RMSEA <= 0.05 0.048
Standardized Root Mean Square Residual:
SRMR 0.085
Parameter Estimates:
Information Expected
Information saturated (h1) model Structured
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intention =~
I2 1.000 1.895 0.697
A8 0.782 0.064 12.245 0.000 1.482 0.866
A14 0.666 0.063 10.518 0.000 1.262 0.723
Hagerbaum =~
H1 1.000 1.176 0.882
H2 0.486 0.053 9.210 0.000 0.572 0.559
H3 0.912 0.056 16.385 0.000 1.073 0.804
H4 1.082 0.050 21.679 0.000 1.273 0.909
H5 0.766 0.070 10.913 0.000 0.901 0.632
H6 1.027 0.054 19.084 0.000 1.207 0.862
Attitude =~
A1 1.000 1.000 0.534
A5 1.339 0.143 9.389 0.000 1.339 0.651
A6 1.011 0.109 9.281 0.000 1.011 0.644
PerceivedBehavioralControl =~
A3 1.000 1.000 0.509
A10 1.688 0.149 11.364 0.000 1.688 0.914
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Hagerbaum ~
Intention 0.397 0.070 5.662 0.000 0.640 0.640
PrcvdBhvrlCntr -0.234 0.128 -1.833 0.067 -0.199 -0.199
Intention ~
Attitude 1.094 0.229 4.768 0.000 0.577 0.577
PrcvdBhvrlCntr 0.564 0.204 2.762 0.006 0.298 0.298
A9 0.120 0.048 2.477 0.013 0.063 0.139
SS -0.039 0.021 -1.851 0.064 -0.021 -0.106
JD 0.017 0.041 0.417 0.676 0.009 0.026
WJI 0.014 0.055 0.250 0.803 0.007 0.014
WTC -0.083 0.045 -1.859 0.063 -0.044 -0.119
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Attitude ~~
PrcvdBhvrlCntr 0.660 0.073 8.994 0.000 0.660 0.660
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.I2 3.803 0.420 9.055 0.000 3.803 0.514
.A8 0.732 0.127 5.755 0.000 0.732 0.250
.A14 1.452 0.166 8.727 0.000 1.452 0.477
.H1 0.394 0.050 7.852 0.000 0.394 0.222
.H2 0.720 0.071 10.132 0.000 0.720 0.688
.H3 0.631 0.069 9.107 0.000 0.631 0.354
.H4 0.340 0.050 6.860 0.000 0.340 0.174
.H5 1.222 0.122 9.978 0.000 1.222 0.601
.H6 0.503 0.061 8.273 0.000 0.503 0.256
.A1 2.500 0.266 9.414 0.000 2.500 0.714
.A5 2.438 0.307 7.942 0.000 2.438 0.576
.A6 1.442 0.179 8.035 0.000 1.442 0.585
.A3 2.859 0.299 9.569 0.000 2.859 0.741
.A10 0.560 0.368 1.520 0.129 0.560 0.164
.Intention 1.000 0.278 0.278
.Hagerbaum 1.000 0.723 0.723
Attitude 1.000 1.000 1.000
PrcvdBhvrlCntr 1.000 1.000 1.000
Terrence Jorgensen
Aug 3, 2018, 8:17:34 AM8/3/18
to lavaan
My model shows negative covariances for the observed variables but I do not understand why
Your model only estimates one covariance, and it is between latent, not observed, variables.
Covariances:Estimate Std.Err z-value P(>|z|) Std.lv Std.allAttitude ~~PrcvdBhvrlCntr 0.660 0.073 8.994 0.000 0.660 0.660
Are you referring to the model-implied correlations?
inspect(MODELWSPISNPBCATTINTHAG,"cor.all")
I don't see why that would be a problem. Are the observed covariances not negative for the same observed-variable pairs?
lavInspect(MODELWSPISNPBCATTINTHAG, "sampstat")You can see how much the model-implied values differ from the observed values:
resid(MODELWSPISNPBCATTINTHAG)In a correlation metric:
resid(MODELWSPISNPBCATTINTHAG, type = "cor")Terrence D. Jorgensen
Postdoctoral Researcher, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
UvA web page: http://www.uva.nl/profile/t.d.jorgensen
Aryanne van Delft
Aug 6, 2018, 9:22:55 AM8/6/18
to lavaan
I thought that estimating covariances is the default setting of lavaan? When I draw a path digram via semPaths(MODELWSPISNPBCATTINTHAG, "model", "standardized estimates"), negative covariances are presented.
I don't see why that would be a problem. Are the observed covariances not negative for the same observed-variable pairs?
Some of the covariances are negative
lavInspect(MODELWSPISNPBCATTINTHAG, "sampstat")
resid(MODELWSPISNPBCATTINTHAG)
resid(MODELWSPISNPBCATTINTHAG, type = "cor")
> lavInspect(MODELWSPISNPBCATTINTHAG, "sampstat")
$`cov`
I2 A8 A14 H1 H2 H3 H4 H5 H6 A1 A5 A6 A3 A10 A9 SS JD WJI WTC
I2 7.461
A8 2.893 2.955
A14 2.631 1.800 3.065
H1 1.400 0.948 0.701 1.381
H2 0.609 0.582 0.474 0.512 0.994
H3 1.256 0.795 0.711 0.914 0.667 1.599
H4 1.503 1.036 0.838 1.174 0.596 1.157 1.703
H5 1.272 0.775 0.672 0.743 0.462 0.879 0.920 1.904
H6 1.374 0.734 0.719 1.128 0.484 1.087 1.286 1.004 1.728
A1 1.449 0.917 0.733 0.360 0.201 0.293 0.216 0.352 0.342 3.239
A5 1.600 1.507 1.376 0.377 0.329 0.471 0.499 0.515 0.395 1.425 4.190
A6 1.445 1.295 1.224 0.373 0.305 0.323 0.567 0.522 0.405 0.633 1.280 2.442
A3 0.831 1.162 0.889 0.366 0.186 -0.061 0.379 -0.061 -0.008 0.696 1.341 1.007 4.236
A10 1.773 1.828 1.587 0.601 0.278 0.300 0.575 0.335 0.361 0.838 1.460 1.203 2.071 3.518
A9 0.998 1.110 1.229 0.487 0.408 0.475 0.510 0.684 0.739 0.305 0.735 0.829 -0.344 0.696 4.809
SS -1.967 -0.840 0.417 -0.728 -0.605 -1.083 -1.333 -0.191 -1.063 0.319 1.109 0.182 1.338 0.274 -0.758 26.366
JD 0.962 0.636 0.820 0.439 0.148 0.482 0.904 0.889 0.796 -0.054 0.764 0.375 -0.745 0.024 1.956 -2.171 8.527
WJI 0.324 -0.067 -0.276 0.086 0.168 0.180 0.134 0.051 0.199 -0.346 -0.711 -0.391 -0.387 -0.087 0.362 -3.674 -0.326 3.742
WTC -0.752 -0.460 -0.340 -0.327 -0.110 -0.427 -0.680 -0.462 -0.692 0.138 -0.008 0.440 1.325 0.534 -1.913 3.496 -4.209 -0.679 7.379
$mean
I2 A8 A14 H1 H2 H3 H4 H5 H6 A1 A5 A6 A3 A10 A9 SS JD WJI WTC
6.982 6.868 6.799 3.128 1.566 2.242 2.785 2.370 2.717 3.580 6.621 7.365 4.744 6.082 5.868 33.553 12.425 5.219 11.557
> resid(MODELWSPISNPBCATTINTHAG)
$`type`
[1] "raw"
$cov
I2 A8 A14 H1 H2 H3 H4 H5 H6 A1 A5 A6 A3 A10 A9 SS JD WJI WTC
I2 0.067
A8 0.084 0.027
A14 0.239 -0.070 0.020
H1 0.273 0.068 -0.049 -0.395
H2 0.061 0.154 0.110 -0.160 -0.052
H3 0.228 -0.009 0.026 -0.347 0.053 -0.183
H4 0.284 0.082 0.026 -0.323 -0.131 -0.208 -0.258
H5 0.409 0.100 0.098 -0.316 -0.053 -0.088 -0.227 -0.129
H6 0.217 -0.170 -0.051 -0.292 -0.206 -0.208 -0.250 -0.083 -0.232
A1 -0.017 -0.230 -0.244 -0.069 -0.007 -0.097 -0.248 0.024 -0.098 -0.261
A5 -0.362 -0.028 0.069 -0.196 0.050 -0.052 -0.122 0.075 -0.194 0.087 -0.040
A6 -0.038 0.135 0.236 -0.060 0.094 -0.073 0.098 0.191 -0.040 -0.378 -0.074 -0.023
A3 -0.455 0.157 0.033 0.089 0.051 -0.314 0.079 -0.273 -0.293 0.037 0.459 0.340 0.377
A10 -0.398 0.131 0.142 0.133 0.050 -0.127 0.068 -0.023 -0.119 -0.275 -0.030 0.077 0.383 0.110
A9 0.194 0.482 0.694 0.168 0.253 0.184 0.165 0.439 0.411 0.305 0.735 0.829 -0.344 0.696 0.000
SS -0.464 0.335 1.418 -0.131 -0.315 -0.539 -0.687 0.267 -0.450 0.319 1.109 0.182 1.338 0.274 0.000 0.000
JD 0.152 0.003 0.281 0.117 -0.009 0.188 0.556 0.642 0.466 -0.054 0.764 0.375 -0.745 0.024 0.000 0.000 0.000
WJI 0.033 -0.294 -0.469 -0.029 0.112 0.075 0.009 -0.037 0.081 -0.346 -0.711 -0.391 -0.387 -0.087 0.000 0.000 0.000 0.000
WTC 0.308 0.369 0.366 0.095 0.095 -0.043 -0.223 -0.139 -0.259 0.138 -0.008 0.440 1.325 0.534 0.000 0.000 0.000 0.000 0.000
$mean
I2 A8 A14 H1 H2 H3 H4 H5 H6 A1 A5 A6 A3 A10 A9 SS JD WJI WTC
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> resid(MODELWSPISNPBCATTINTHAG, type = "cor")
$`type`
[1] "cor.bollen"
$cor
I2 A8 A14 H1 H2 H3 H4 H5 H6 A1 A5 A6 A3 A10 A9 SS JD WJI WTC
I2 0.000
A8 0.012 0.000
A14 0.046 -0.028 0.000
H1 0.125 0.083 0.018 0.000
H2 0.027 0.095 0.068 -0.056 0.000
H3 0.080 0.014 0.027 -0.094 0.080 0.000
H4 0.101 0.064 0.035 -0.037 -0.050 -0.029 0.000
H5 0.115 0.050 0.048 -0.099 -0.017 -0.004 -0.063 0.000
H6 0.079 -0.053 -0.003 -0.031 -0.112 -0.039 -0.034 0.009 0.000
A1 0.007 -0.062 -0.066 -0.002 0.003 -0.028 -0.085 0.019 -0.023 0.000
A5 -0.065 -0.008 0.020 -0.052 0.029 -0.009 -0.029 0.032 -0.058 0.039 0.000
A6 -0.009 0.050 0.087 -0.004 0.064 -0.025 0.065 0.094 -0.005 -0.119 -0.019 0.000
A3 -0.093 0.029 -0.003 0.045 0.024 -0.120 0.032 -0.097 -0.107 0.008 0.100 0.097 0.000
A10 -0.086 0.030 0.035 0.083 0.028 -0.047 0.039 -0.007 -0.039 -0.074 -0.012 0.022 0.071 0.000
A9 0.032 0.127 0.180 0.080 0.117 0.072 0.066 0.148 0.149 0.077 0.164 0.242 -0.076 0.169 0.000
SS -0.033 0.039 0.158 -0.033 -0.063 -0.087 -0.109 0.036 -0.072 0.035 0.106 0.023 0.127 0.028 0.000 0.000
JD 0.019 0.000 0.055 0.045 -0.002 0.055 0.152 0.161 0.127 -0.010 0.128 0.082 -0.124 0.004 0.000 0.000 0.000
WJI 0.006 -0.089 -0.139 -0.007 0.059 0.033 0.007 -0.013 0.035 -0.099 -0.180 -0.129 -0.097 -0.024 0.000 0.000 0.000 0.000
WTC 0.042 0.080 0.077 0.014 0.033 -0.018 -0.072 -0.040 -0.080 0.028 -0.001 0.104 0.237 0.105 0.000 0.000 0.000 0.000 0.000
$mean
I2 A8 A14 H1 H2 H3 H4 H5 H6 A1 A5 A6 A3 A10 A9 SS JD WJI WTC
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Terrence Jorgensen
Aug 7, 2018, 8:14:51 AM8/7/18
to lavaan
I thought that estimating covariances is the default setting of lavaan?
Only among exogenous latent variables, of which you only have 2.
Some of the covariances are negative
Then it sounds like there is nothing wrong with expecting the model-implied covariances to be negative too. If your model fits well, it should reproduce your observed sample statistics.
Aryanne van Delft
Aug 8, 2018, 8:29:15 AM8/8/18
to lavaan
Thanks a lot !!!
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