SEM with categorical, non-normal variables and missing data

Sin Ching See

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Mar 9, 2019, 1:14:09 AM3/9/19

to lavaan

Hi all,

I am trying to run SEM on my dataset (n = 501). There are several issues with my data so the default ML doesn't seem to be an appropriate estimator:

1. My data is mostly categorical and non-normal. In the diagram below, I have indicated the nature of each of my variable (in red). Also, for my final outcome variable (currentbehav), it is a latent variable made up of an ordered variable (Freq of visit) and a binary variable (Fav activity), which I makes me wonder what the nature of the final outcome variable is.

2. I have missing data in several of my variables, a large proportion of it comes from the variable HHincomeperpersonK (household income per person) and favourite activity - young and now. I have checked my missing data, and it is unlikely to be missing completely at random (MCAR), so I think I should use FIML for the model.

I specified the model as follows and ran a SEM on it.

VBNfullmodel <-'

#measurement model

socioecon =~ Gender + Age + Nationality + Ethnicity + Religion + Relationship + HHincomeperpersonK + Housing_type

personality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative

NEP=~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis

pastexposure =~ Act_after_school_outdoors + Freq_of_visit_young + Fav_activity_Young + Childhood_memory

currentbehav =~ 1*Freq_of_visit_now + 1*Fav_acitivity_Now

#regression

currentbehav ~ NEP

NEP ~ Instrumental + Relational + Intrinsic

Instrumental ~ personality + pastexposure

Relational ~ personality + pastexposure

Intrinsic ~ personality + pastexposure

personality ~ socioecon + pastexposure

pastexposure ~ socioecon

'

The code runs fine with no warning messages using ML as an estimator. However, I think the estimates produced using ML are unlikely to be reliable given that my final outcome variable (currentbehav) is not normal or continuous. After reading some threads from this google group and some SEM textbooks and guides, I decide to use MLR as an estimation method since I have missing data and MLR seems to be able to deal with it using FIML. However, when I changed the estimator to MLR, many warning messages were produced.

fit7 <- sem(VBNfullmodel, data = fulldata, orthogonal = TRUE, "MLR")

I am not sure if MLR is the appropriate estimation method in my case. I checked several model fit indices and found that the model using MLR has better fit index than the model using ML (although i'm not sure if i'm suppose to compare it this way) I am also thinking if my model is too complex, and if I should try to simplify it a little.

I will greatly appreciate any advice/comment. Thank you in advance!

Sin Ching See

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Mar 9, 2019, 8:56:55 AM3/9/19

to lavaan

fit5 <- sem(VBNfullmodel, data = fulldata, orthogonal = TRUE)

summary(fit5, standardized = TRUE, fit.measures = TRUE)

lavaan 0.6-3 ended normally after 180 iterations

Optimization method NLMINB

Number of free parameters 96

Used Total

Number of observations 280 501

Estimator ML

Model Fit Test Statistic 1997.188

Degrees of freedom 850

P-value (Chi-square) 0.000

Model test baseline model:

Minimum Function Test Statistic 3222.475

Degrees of freedom 903

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.505

Tucker-Lewis Index (TLI) 0.475

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -15062.540

Loglikelihood unrestricted model (H1) -14063.946

Number of free parameters 96

Akaike (AIC) 30317.080

Bayesian (BIC) 30666.020

Sample-size adjusted Bayesian (BIC) 30361.610

Root Mean Square Error of Approximation:

RMSEA 0.069

90 Percent Confidence Interval 0.065 0.073

P-value RMSEA <= 0.05 0.000

Standardized Root Mean Square Residual:

SRMR 0.088

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

socioecon =~

Male 1.000 0.443 0.886

Age 2.829 1.193 2.372 0.018 1.252 0.530

Singaporean 0.033 0.042 0.771 0.441 0.014 0.054

Chinese 0.089 0.051 1.737 0.082 0.039 0.150

Hokkien 0.082 0.080 1.018 0.308 0.036 0.073

NoReligion 0.116 0.084 1.384 0.166 0.052 0.107

Single -0.057 0.068 -0.844 0.399 -0.025 -0.059

HHincomprprsnK 0.172 0.243 0.707 0.480 0.076 0.049

Housing_type -0.116 0.479 -0.241 0.809 -0.051 -0.016

personality =~

Extrvrtd_Enths 1.000 0.634 0.385

Criticl_qrrlsm -0.402 0.194 -2.076 0.038 -0.255 -0.156

Dpndbl_Slfdscp 0.718 0.182 3.947 0.000 0.455 0.363

Anxious_slypst -0.498 0.198 -2.520 0.012 -0.316 -0.195

Opentnwx_cmplx 0.691 0.175 3.943 0.000 0.438 0.362

Reserved_quiet -0.843 0.228 -3.703 0.000 -0.534 -0.327

Sympathetc_wrm 0.520 0.155 3.344 0.001 0.329 0.281

Disrgnsd_crlss -0.440 0.201 -2.194 0.028 -0.279 -0.166

Clm_mtnllystbl 0.670 0.191 3.500 0.000 0.424 0.300

Convntnl_ncrtv -0.342 0.167 -2.053 0.040 -0.217 -0.154

NEP =~

Limit 1.000 0.401 0.432

Modify -0.243 0.190 -1.279 0.201 -0.097 -0.086

Interfere 0.948 0.202 4.684 0.000 0.380 0.383

Ingenuity -0.186 0.188 -0.989 0.323 -0.074 -0.066

Abuse 1.296 0.202 6.408 0.000 0.520 0.719

NatRes 0.231 0.176 1.311 0.190 0.093 0.088

Rights 0.911 0.193 4.728 0.000 0.365 0.388

Industrial -0.802 0.237 -3.385 0.001 -0.322 -0.247

Laws 0.851 0.162 5.270 0.000 0.341 0.464

Crisis -0.684 0.217 -3.156 0.002 -0.274 -0.228

Spaceship 1.130 0.203 5.571 0.000 0.453 0.514

Rule -0.496 0.226 -2.195 0.028 -0.199 -0.151

Balance 0.828 0.171 4.840 0.000 0.332 0.402

Learn -0.213 0.183 -1.163 0.245 -0.085 -0.078

Eco_crsis 1.443 0.220 6.555 0.000 0.579 0.789

pastexposure =~

Frq_f_vst_ynCK 1.000 0.478 0.443

Act_ftr_schl_t 0.524 0.104 5.019 0.000 0.251 0.553

NtrApprctn_Yng -0.028 0.049 -0.572 0.567 -0.013 -0.042

Childhood_mmry 1.198 0.241 4.977 0.000 0.573 0.541

currentbehav =~

NatrApprctn_Nw 1.000 0.096 0.250

Frq_f_vst_nwCK -0.674 0.794 -0.849 0.396 -0.065 -0.109

Regressions:

Estimate Std.Err z-value P(>|z|) Std.lv Std.all

currentbehav ~

NEP 0.134 0.066 2.039 0.041 0.559 0.559

NEP ~

Instrumental -0.093 0.105 -0.891 0.373 -0.233 -0.109

Relational 0.015 0.083 0.177 0.860 0.037 0.020

Intrinsic 0.198 0.079 2.498 0.013 0.494 0.252

Instrumental ~

personality 3.464 1.741 1.989 0.047 2.195 4.712

pastexposure -4.193 2.363 -1.775 0.076 -2.006 -4.307

Relational ~

personality 3.488 1.746 1.997 0.046 2.210 4.161

pastexposure -4.167 2.367 -1.760 0.078 -1.994 -3.754

Intrinsic ~

personality 3.134 1.589 1.972 0.049 1.986 3.892

pastexposure -3.848 2.159 -1.782 0.075 -1.841 -3.609

personality ~

socioecon 0.013 0.022 0.613 0.540 0.009 0.009

pastexposure 1.299 0.308 4.222 0.000 0.981 0.981

pastexposure ~

socioecon 0.101 0.098 1.036 0.300 0.094 0.094

Variances:

Estimate Std.Err z-value P(>|z|) Std.lv Std.all

.Male 0.054 0.081 0.664 0.507 0.054 0.215

.Age 4.008 0.731 5.485 0.000 4.008 0.719

.Singaporean 0.072 0.006 11.823 0.000 0.072 0.997

.Chinese 0.068 0.006 11.720 0.000 0.068 0.978

.Hokkien 0.244 0.021 11.814 0.000 0.244 0.995

.NoReligion 0.230 0.020 11.787 0.000 0.230 0.989

.Single 0.181 0.015 11.821 0.000 0.181 0.997

.HHincomprprsnK 2.424 0.205 11.825 0.000 2.424 0.998

.Housing_type 10.049 0.849 11.831 0.000 10.049 1.000

.Extrvrtd_Enths 2.311 0.210 10.998 0.000 2.311 0.852

.Criticl_qrrlsm 2.615 0.223 11.716 0.000 2.615 0.976

.Dpndbl_Slfdscp 1.368 0.123 11.108 0.000 1.368 0.869

.Anxious_slypst 2.523 0.217 11.646 0.000 2.523 0.962

.Opentnwx_cmplx 1.273 0.115 11.111 0.000 1.273 0.869

.Reserved_quiet 2.385 0.212 11.263 0.000 2.385 0.893

.Sympathetc_wrm 1.267 0.111 11.427 0.000 1.267 0.921

.Disrgnsd_crlss 2.758 0.236 11.700 0.000 2.758 0.973

.Clm_mtnllystbl 1.821 0.160 11.363 0.000 1.821 0.910

.Convntnl_ncrtv 1.946 0.166 11.719 0.000 1.946 0.976

.Limit 0.701 0.063 11.201 0.000 0.701 0.813

.Modify 1.277 0.108 11.812 0.000 1.277 0.993

.Interfere 0.844 0.074 11.363 0.000 0.844 0.854

.Ingenuity 1.266 0.107 11.820 0.000 1.266 0.996

.Abuse 0.253 0.029 8.746 0.000 0.253 0.483

.NatRes 1.100 0.093 11.811 0.000 1.100 0.992

.Rights 0.754 0.066 11.347 0.000 0.754 0.849

.Industrial 1.588 0.136 11.655 0.000 1.588 0.939

.Laws 0.425 0.038 11.077 0.000 0.425 0.785

.Crisis 1.380 0.118 11.683 0.000 1.380 0.948

.Spaceship 0.572 0.053 10.838 0.000 0.572 0.736

.Rule 1.689 0.144 11.768 0.000 1.689 0.977

.Balance 0.572 0.051 11.302 0.000 0.572 0.838

.Learn 1.192 0.101 11.816 0.000 1.192 0.994

.Eco_crsis 0.203 0.028 7.185 0.000 0.203 0.378

.Frq_f_vst_ynCK 0.940 0.091 10.365 0.000 0.940 0.804

.Act_ftr_schl_t 0.143 0.016 9.147 0.000 0.143 0.694

.NtrApprctn_Yng 0.101 0.009 11.822 0.000 0.101 0.998

.Childhood_mmry 0.796 0.085 9.315 0.000 0.796 0.708

.NatrApprctn_Nw 0.140 0.025 5.624 0.000 0.140 0.938

.Frq_f_vst_nwCK 0.354 0.031 11.228 0.000 0.354 0.988

.Instrumental 0.024 0.008 3.186 0.001 0.024 0.112

.Relational 0.078 0.010 7.853 0.000 0.078 0.278

.Intrinsic 0.109 0.011 9.803 0.000 0.109 0.419

socioecon 0.196 0.083 2.351 0.019 1.000 1.000

.personality 0.014 0.015 0.967 0.333 0.035 0.035

.NEP 0.155 0.045 3.425 0.001 0.961 0.961

.pastexposure 0.227 0.073 3.123 0.002 0.991 0.991

.currentbehav 0.006 0.022 0.293 0.770 0.687 0.687

Mauricio Garnier-Villarreal

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Mar 9, 2019, 1:06:51 PM3/9/19

to lavaan

If you have ordered categorical data, the best option is to use Diagonal weighted least square estimator (WLSM). Now, the issue with missing data is that since it is not a Maximum likelihood method FIML is not an option. You would need to use Multiple imputations. For this you can use the sem.mi function in the semTools package. I recommned to use the 2 step process, first generate the imputed data sets, for example with the mice package, and then give the imputations to the sem.mi function to do the analysis with the multiple data sets and combine the results with WLSMV

Sin Ching See

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Mar 10, 2019, 11:34:10 AM3/10/19

to lavaan

Thank you for the clear instruction! I have tried using Diagonal weighted least square (which I think is DWLS for sem) and have also used mice for multiple imputations of missing data. However, there are many warning messages produced and I'm not sure what I should do next. The output and warning messages are as follows:

fit9 <- sem.mi(VBNfullmodel, data= mi_list, estimator ="DWLS", orthogonal = TRUE,

ordered = c("Freq_of_visit_nowOrd", "Freq_of_visit_youngOrd", "NatureAppreciation_Now", "NatureAppreciation_Young", "Act_after_school_outdoors", "Childhood_memory",

"Extraverted_Enthusiastic", "Critical_quarrelsome", "Dependable_Selfdiscipline", "Anxious_easilyupset", "Opentonewex_complex", "Reserved_quiet", "Sympathetic_warm", "Disorganised_careless", "Calm_emotionallystable", "Conventional_uncreative",

"Limit", "Modify", "Interfere", "Ingenuity", "Abuse", "NatRes", "Rights", "Industrial", "Laws", "Crisis", "Spaceship", "Rule", "Balance", "Learn", "Eco_crsis",

"Male", "Single", "Housing_type"

))

There were 24 warnings (use warnings() to see them)

> warnings()

Warning messages:

1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

2: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

3: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

4: In lavaan::lavaan(model = "\n#measurement model \nsocioecon =~ Male + Age + Single + HHincomeperpersonK + Housing_type\npersonality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative\nNEP=~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis\npastexposure =~ Freq_of_visit_youngOrd + Act_after_school_outdoors + NatureAppreciation_Young + Childhood_memory \ncurrentbehav =~ NatureAppreciation_Now + Freq_of_visit_nowOrd\n\n#regression \ncurrentbehav ~ NEP \nNEP ~ Instrumental + Relational + Intrinsic \nInstrumental ~ personality + pastexposure \nRelational ~ personality + pastexposure \nIntrinsic ~ personality + pastexposure \npersonality ~ socioecon + pastexposure\npastexposure ~ socioecon\n", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

5: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

6: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

7: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

8: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

9: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

10: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

11: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

12: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

13: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

14: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

15: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

16: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

17: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

18: In sqrt(ETA2) : NaNs produced

19: In sqrt(ETA2) : NaNs produced

20: In sqrt(ETA2) : NaNs produced

21: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

22: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

23: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

24: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

summary(fit9)

Convergence information:

The model converged on 5 imputed data sets

Standard errors could not be computed for data set(s) 1, 2, 3, 5

Try fitting the model to the individual data set(s) to diagnose problems. If they cannot be fixed, try inspecting the imputations. It may be necessary to reimpute the data with some restrictions imposed.

Heywood cases detected for data set(s) 1, 2, 3, 5

These are not necessarily a cause for concern, unless a pooled estimate is also a Heywood case.

Rubin's (1987) rules were used to pool point and SE estimates across 5 imputed data sets, and to calculate degrees of freedom for each parameter's t test and CI.

Parameter Estimates:

Information Expected

Information saturated (h1) model Unstructured

Standard Errors Standard

Latent Variables:

Estimate Std.Err t-value df P(>|t|)

socioecon =~

Male 1.000

Age -76.581 329.209 -0.233 NA NA

Single -0.050 14.970 -0.003 NA NA

HHincomprprsnK -0.056 14.907 -0.004 NA NA

Housing_type 0.012 8.383 0.001 NA NA

personality =~

Extrvrtd_Enths 1.000

Criticl_qrrlsm -0.224 12.788 -0.017 NA NA

Dpndbl_Slfdscp 0.902 18.849 0.048 NA NA

Anxious_slypst -0.583 15.102 -0.039 NA NA

Opentnwx_cmplx 0.704 16.742 0.042 NA NA

Reserved_quiet -0.676 16.591 -0.041 NA NA

Sympathetc_wrm 0.679 16.116 0.042 NA NA

Disrgnsd_crlss -0.623 15.382 -0.040 NA NA

Clm_mtnllystbl 0.732 16.293 0.045 NA NA

Convntnl_ncrtv -0.229 13.001 -0.018 NA NA

NEP =~

Limit 1.000

Modify -0.688 14.088 -0.049 NA NA

Interfere 0.891 15.369 0.058 NA NA

Ingenuity -0.690 13.512 -0.051 NA NA

Abuse 1.414 19.562 0.072 NA NA

NatRes -0.111 11.328 -0.010 NA NA

Rights 0.907 15.603 0.058 NA NA

Industrial -1.060 16.042 -0.066 NA NA

Laws 0.954 15.641 0.061 NA NA

Crisis -1.202 17.186 -0.070 NA NA

Spaceship 0.831 14.965 0.056 NA NA

Rule -0.852 14.985 -0.057 NA NA

Balance 0.792 14.606 0.054 NA NA

Learn -0.717 13.498 -0.053 NA NA

Eco_crsis 1.531 21.218 0.072 NA NA

pastexposure =~

Frq_f_vst_yngO 1.000

Act_ftr_schl_t 1.218 27.356 0.045 NA NA

NtrApprctn_Yng -0.258 23.408 -0.011 NA NA

Childhood_mmry 1.052 22.516 0.047 NA NA

currentbehav =~

NatrApprctn_Nw 1.000

Frq_f_vst_nwOr 0.400 31.514 0.013 NA NA

Regressions:

Estimate Std.Err t-value df P(>|t|)

currentbehav ~

NEP 0.403 18.462 0.022 NA NA

NEP ~

Instrumental -347.255 48.513 -7.158 NA NA

Relational 320.378 26.176 12.239 NA NA

Intrinsic -0.658 33.511 -0.020 NA NA

Instrumental ~

personality -4.797 195.095 -0.025 NA NA

pastexposure 6.307 220.417 0.029 NA NA

Relational ~

personality -5.134 195.332 -0.026 NA NA

pastexposure 6.769 221.153 0.031 NA NA

Intrinsic ~

personality -4.646 215.469 -0.022 NA NA

pastexposure 6.022 243.228 0.025 NA NA

personality ~

socioecon 0.008 1.093 0.007 NA NA

pastexposure 1.186 24.030 0.049 NA NA

pastexposure ~

socioecon 0.030 2.828 0.010 NA NA

Intercepts:

Estimate Std.Err t-value df P(>|t|)

.Male 0.000

.Age 21.294 30.361 0.701 NA NA

.Single 0.000

.HHincomprprsnK 2.118 26.974 0.079 NA NA

.Housing_type 0.000

.Extrvrtd_Enths 0.000

.Criticl_qrrlsm 0.000

.Dpndbl_Slfdscp 0.000

.Anxious_slypst 0.000

.Opentnwx_cmplx 0.000

.Reserved_quiet 0.000

.Sympathetc_wrm 0.000

.Disrgnsd_crlss 0.000

.Clm_mtnllystbl 0.000

.Convntnl_ncrtv 0.000

.Limit 0.000

.Modify 0.000

.Interfere 0.000

.Ingenuity 0.000

.Abuse 0.000

.NatRes 0.000

.Rights 0.000

.Industrial 0.000

.Laws 0.000

.Crisis 0.000

.Spaceship 0.000

.Rule 0.000

.Balance 0.000

.Learn 0.000

.Eco_crsis 0.000

.Frq_f_vst_yngO 0.000

.Act_ftr_schl_t 0.000

.NtrApprctn_Yng 0.000

.Childhood_mmry 0.000

.NatrApprctn_Nw 0.000

.Frq_f_vst_nwOr 0.000

.Instrumental 3.959 9.471 0.418 NA NA

.Relational 3.868 10.055 0.385 NA NA

.Intrinsic 4.172 10.493 0.398 NA NA

socioecon 0.000

.personality 0.000

.NEP 0.000

.pastexposure 0.000

.currentbehav 0.000

Thresholds:

Estimate Std.Err t-value df P(>|t|)

Male|t1 -0.065 14.224 -0.005 NA NA

Single|t1 -0.865 16.401 -0.053 NA NA

Housing_typ|t1 -2.597 51.544 -0.050 NA NA

Housing_typ|t2 -1.833 26.250 -0.070 NA NA

Housing_typ|t3 -1.782 25.388 -0.070 NA NA

Housing_typ|t4 -1.758 25.001 -0.070 NA NA

Housing_typ|t5 -0.986 16.889 -0.058 NA NA

Housing_typ|t6 -0.960 16.746 -0.057 NA NA

Housing_typ|t7 -0.693 15.433 -0.045 NA NA

Housing_typ|t8 0.107 14.254 0.007 NA NA

Housing_typ|t9 0.826 16.067 0.051 NA NA

Housng_typ|t10 0.878 16.322 0.054 NA NA

Housng_typ|t11 0.893 16.401 0.054 NA NA

Housng_typ|t12 0.902 16.482 0.055 NA NA

Extrvrtd_Ent|1 -1.775 26.250 -0.068 NA NA

Extrvrtd_Ent|2 -0.734 15.694 -0.047 NA NA

Extrvrtd_Ent|3 -0.225 14.343 -0.016 NA NA

Extrvrtd_Ent|4 0.053 14.219 0.004 NA NA

Extrvrtd_Ent|5 0.627 15.274 0.041 NA NA

Extrvrtd_Ent|6 1.775 26.250 0.068 NA NA

Crtcl_qrrlsm|1 -1.393 20.553 -0.068 NA NA

Crtcl_qrrlsm|2 -0.670 15.433 -0.043 NA NA

Crtcl_qrrlsm|3 -0.189 14.304 -0.013 NA NA

Crtcl_qrrlsm|4 0.184 14.299 0.013 NA NA

Crtcl_qrrlsm|5 1.038 17.375 0.060 NA NA

Crtcl_qrrlsm|6 1.912 29.136 0.066 NA NA

Dpndbl_Slfds|1 -2.145 35.572 -0.060 NA NA

Dpndbl_Slfds|2 -1.608 23.391 -0.069 NA NA

Dpndbl_Slfds|3 -1.055 17.496 -0.060 NA NA

Dpndbl_Slfds|4 -0.608 15.210 -0.040 NA NA

Dpndbl_Slfds|5 0.148 14.269 0.010 NA NA

Dpndbl_Slfds|6 1.448 21.198 0.068 NA NA

Anxs_slypst|t1 -1.556 22.621 -0.069 NA NA

Anxs_slypst|t2 -0.794 15.967 -0.050 NA NA

Anxs_slypst|t3 -0.350 14.532 -0.024 NA NA

Anxs_slypst|t4 0.018 14.213 0.001 NA NA

Anxs_slypst|t5 0.850 16.246 0.052 NA NA

Anxs_slypst|t6 1.523 22.168 0.069 NA NA

Opntnwx_cmpl|1 -2.879 79.970 -0.036 NA NA

Opntnwx_cmpl|2 -2.015 31.714 -0.064 NA NA

Opntnwx_cmpl|3 -1.238 18.977 -0.065 NA NA

Opntnwx_cmpl|4 -0.682 15.482 -0.044 NA NA

Opntnwx_cmpl|5 0.230 14.349 0.016 NA NA

Opntnwx_cmpl|6 1.196 18.603 0.064 NA NA

Reserved_qt|t1 -1.826 27.255 -0.067 NA NA

Reserved_qt|t2 -1.156 18.267 -0.063 NA NA

Reserved_qt|t3 -0.708 15.585 -0.045 NA NA

Reserved_qt|t4 -0.307 14.459 -0.021 NA NA

Reserved_qt|t5 0.376 14.584 0.026 NA NA

Reserved_qt|t6 1.318 19.744 0.067 NA NA

Sympthtc_wrm|1 -2.327 42.365 -0.055 NA NA

Sympthtc_wrm|2 -1.800 26.732 -0.067 NA NA

Sympthtc_wrm|3 -1.318 19.744 -0.067 NA NA

Sympthtc_wrm|4 -0.754 15.780 -0.048 NA NA

Sympthtc_wrm|5 0.033 14.215 0.002 NA NA

Sympthtc_wrm|6 1.186 18.516 0.064 NA NA

Dsrgnsd_crls|1 -1.448 21.198 -0.068 NA NA

Dsrgnsd_crls|2 -0.689 15.507 -0.044 NA NA

Dsrgnsd_crls|3 -0.168 14.285 -0.012 NA NA

Dsrgnsd_crls|4 0.184 14.299 0.013 NA NA

Dsrgnsd_crls|5 0.917 16.610 0.055 NA NA

Dsrgnsd_crls|6 1.800 26.732 0.067 NA NA

Clm_mtnllyst|1 -2.198 37.360 -0.059 NA NA

Clm_mtnllyst|2 -1.507 21.957 -0.069 NA NA

Clm_mtnllyst|3 -0.822 16.102 -0.051 NA NA

Clm_mtnllyst|4 -0.387 14.606 -0.027 NA NA

Clm_mtnllyst|5 0.425 14.689 0.029 NA NA

Clm_mtnllyst|6 1.462 21.376 0.068 NA NA

Cnvntnl_ncrt|1 -1.707 25.001 -0.068 NA NA

Cnvntnl_ncrt|2 -1.004 17.148 -0.059 NA NA

Cnvntnl_ncrt|3 -0.403 14.640 -0.028 NA NA

Cnvntnl_ncrt|4 0.204 14.320 0.014 NA NA

Cnvntnl_ncrt|5 1.064 17.558 0.061 NA NA

Cnvntnl_ncrt|6 2.145 35.572 0.060 NA NA

Limit|t1 -140.285 36.388 -3.855 NA NA

Limit|t2 -139.830 29.494 -4.741 NA NA

Limit|t3 -139.164 25.370 -5.485 NA NA

Limit|t4 -138.036 24.206 -5.703 NA NA

Modify|t1 93.793 25.938 3.616 NA NA

Modify|t2 94.852 20.740 4.573 NA NA

Modify|t3 95.273 20.441 4.661 NA NA

Modify|t4 96.573 24.610 3.924 NA NA

Interfere|t1 -125.305 38.394 -3.264 NA NA

Interfere|t2 -124.468 26.086 -4.771 NA NA

Interfere|t3 -124.016 23.868 -5.196 NA NA

Interfere|t4 -122.793 22.971 -5.346 NA NA

Ingenuity|t1 94.294 25.122 3.753 NA NA

Ingenuity|t2 95.240 20.640 4.614 NA NA

Ingenuity|t3 95.855 20.317 4.718 NA NA

Ingenuity|t4 96.993 24.368 3.980 NA NA

Abuse|t1 -198.013 57.783 -3.427 NA NA

Abuse|t2 -197.300 37.372 -5.279 NA NA

Abuse|t3 -196.749 32.341 -6.084 NA NA

Abuse|t4 -195.377 29.751 -6.567 NA NA

NatRes|t1 13.611 27.603 0.493 NA NA

NatRes|t2 14.406 19.014 0.758 NA NA

NatRes|t3 14.977 16.958 0.883 NA NA

NatRes|t4 16.153 17.994 0.898 NA NA

Rights|t1 -127.403 37.452 -3.402 NA NA

Rights|t2 -126.769 27.593 -4.594 NA NA

Rights|t3 -126.370 24.979 -5.059 NA NA

Rights|t4 -125.341 22.979 -5.454 NA NA

Industrial|t1 145.995 25.448 5.737 NA NA

Industrial|t2 146.904 24.650 5.960 NA NA

Industrial|t3 147.300 25.139 5.859 NA NA

Industrial|t4 148.070 28.428 5.209 NA NA

Laws|t1 -134.262 49.717 -2.701 NA NA

Laws|t2 -133.831 35.920 -3.726 NA NA

Laws|t3 -133.113 26.692 -4.987 NA NA

Laws|t4 -131.765 23.392 -5.633 NA NA

Crisis|t1 165.647 27.179 6.095 NA NA

Crisis|t2 166.557 26.585 6.265 NA NA

Crisis|t3 167.091 27.430 6.092 NA NA

Crisis|t4 167.873 31.815 5.277 NA NA

Spaceship|t1 -116.915 36.868 -3.171 NA NA

Spaceship|t2 -116.253 26.553 -4.378 NA NA

Spaceship|t3 -115.710 23.379 -4.949 NA NA

Spaceship|t4 -114.328 22.509 -5.079 NA NA

Rule|t1 117.243 22.770 5.149 NA NA

Rule|t2 117.992 22.281 5.296 NA NA

Rule|t3 118.424 22.901 5.171 NA NA

Rule|t4 119.133 26.202 4.547 NA NA

Balance|t1 -112.160 62.598 -1.792 NA NA

Balance|t2 -110.969 26.827 -4.136 NA NA

Balance|t3 -110.519 23.636 -4.676 NA NA

Balance|t4 -109.109 21.834 -4.997 NA NA

Learn|t1 97.905 25.311 3.868 NA NA

Learn|t2 98.689 21.204 4.654 NA NA

Learn|t3 99.476 20.556 4.839 NA NA

Learn|t4 100.536 24.049 4.181 NA NA

Eco_crsis|t1 -214.119 58.570 -3.656 NA NA

Eco_crsis|t2 -213.406 38.578 -5.532 NA NA

Eco_crsis|t3 -212.793 33.414 -6.368 NA NA

Eco_crsis|t4 -211.629 31.236 -6.775 NA NA

Frq_f_vst_yO|1 -1.646 23.978 -0.069 NA NA

Frq_f_vst_yO|2 -1.417 20.863 -0.068 NA NA

Frq_f_vst_yO|3 -1.213 18.785 -0.065 NA NA

Frq_f_vst_yO|4 -0.873 16.361 -0.053 NA NA

Frq_f_vst_yO|5 -0.367 14.563 -0.025 NA NA

Frq_f_vst_yO|6 0.476 14.810 0.032 NA NA

Frq_f_vst_yO|7 1.315 19.744 0.067 NA NA

Act_ftr_sch_|1 -0.350 14.532 -0.024 NA NA

NtrApprctn_Y|1 1.152 17.892 0.064 NA NA

Chldhd_mmry|t1 -1.271 19.286 -0.066 NA NA

Chldhd_mmry|t2 -0.225 14.343 -0.016 NA NA

Chldhd_mmry|t3 0.664 15.410 0.043 NA NA

Chldhd_mmry|t4 1.686 24.638 0.068 NA NA

NtrApprctn_N|1 -54.388 22.170 -2.453 NA NA

Frq_f_vst_nO|1 -23.758 21.431 -1.109 NA NA

Frq_f_vst_nO|2 -23.557 19.857 -1.186 NA NA

Frq_f_vst_nO|3 -23.278 18.292 -1.273 NA NA

Frq_f_vst_nO|4 -22.770 16.845 -1.352 NA NA

Frq_f_vst_nO|5 -21.994 17.097 -1.286 NA NA

Frq_f_vst_nO|6 -21.977 17.133 -1.283 NA NA

Frq_f_vst_nO|7 -21.237 20.666 -1.028 NA NA

Frq_f_vst_nO|8 -21.226 20.752 -1.023 NA NA

Frq_f_vst_nO|9 -20.540 30.383 -0.676 NA NA

Variances:

Estimate Std.Err t-value df P(>|t|)

.Male 1.188

.Age 128.455 525.868 0.244 NA NA

.Single 1.000

.HHincomprprsnK 3.035 30.456 0.100 NA NA

.Housing_type 1.000

.Extrvrtd_Enths 0.684

.Criticl_qrrlsm 0.984

.Dpndbl_Slfdscp 0.743

.Anxious_slypst 0.892

.Opentnwx_cmplx 0.843

.Reserved_quiet 0.855

.Sympathetc_wrm 0.854

.Disrgnsd_crlss 0.877

.Clm_mtnllystbl 0.831

.Convntnl_ncrtv 0.983

.Limit 0.740

.Modify 0.877

.Interfere 0.794

.Ingenuity 0.876

.Abuse 0.481

.NatRes 0.997

.Rights 0.786

.Industrial 0.708

.Laws 0.764

.Crisis 0.625

.Spaceship 0.821

.Rule 0.812

.Balance 0.837

.Learn 0.867

.Eco_crsis 0.392

.Frq_f_vst_yngO 0.785

.Act_ftr_schl_t 0.681

.NtrApprctn_Yng 0.978

.Childhood_mmry 0.762

.NatrApprctn_Nw 1.005

.Frq_f_vst_nwOr 1.002

.Instrumental 0.007 6.717 0.001 NA NA

.Relational 0.021 7.507 0.003 NA NA

.Intrinsic 0.136 6.648 0.020 NA NA

socioecon -0.188 154.491 -0.001 NA NA

.personality 0.014 1.747 0.008 NA NA

.NEP -1.099 5.630 -0.195 NA NA

.pastexposure 0.215 6.448 0.033 NA NA

.currentbehav -0.047 47.790 -0.001 NA NA

Scales y*:

Estimate Std.Err t-value df P(>|t|)

Male 1.000

Single 1.000

Housing_type 1.000

Extrvrtd_Enths 1.000

Criticl_qrrlsm 1.000

Dpndbl_Slfdscp 1.000

Anxious_slypst 1.000

Opentnwx_cmplx 1.000

Reserved_quiet 1.000

Sympathetc_wrm 1.000

Disrgnsd_crlss 1.000

Clm_mtnllystbl 1.000

Convntnl_ncrtv 1.000

Limit 1.000

Modify 1.000

Interfere 1.000

Ingenuity 1.000

Abuse 1.000

NatRes 1.000

Rights 1.000

Industrial 1.000

Laws 1.000

Crisis 1.000

Spaceship 1.000

Rule 1.000

Balance 1.000

Learn 1.000

Eco_crsis 1.000

Frq_f_vst_yngO 1.000

Act_ftr_schl_t 1.000

NtrApprctn_Yng 1.000

Childhood_mmry 1.000

NatrApprctn_Nw 1.000

Frq_f_vst_nwOr 1.000

Mauricio Garnier-Villarreal

unread,

Mar 11, 2019, 2:13:50 AM3/11/19

to lavaan

First would suggest to change estimator to "WLSMV". This corrects standard erros and fit indices.

second, could you share your imputation code?

...

Sin Ching See

unread,

Mar 11, 2019, 4:42:44 AM3/11/19

to lavaan

I have changed the estimator to "WLSMV" but it seems that there are more warnings now. I also took out a few variables from socio-demo factors because they are not so important and changed freq_of_visit to a dummy coded variable

VBNlessSEmodel <-'

#measurement model

socioecon =~ Male + Age + Single + HHincomeperpersonK + Housing_type

personality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative

NEP=~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis

pastexposure =~ Freq_young_B + Act_after_school_outdoors + NatureAppreciation_Young + Childhood_memory

currentbehav =~ NatureAppreciation_Now + Freq_now_B

#regression

currentbehav ~ NEP

NEP ~ Instrumental + Relational + Intrinsic

Instrumental ~ personality + pastexposure

Relational ~ personality + pastexposure

Intrinsic ~ personality + pastexposure

personality ~ socioecon + pastexposure

pastexposure ~ socioecon

'

fit9 <- sem.mi(VBNlessSEmodel, data= mi_list, estimator ="WLSMV", orthogonal = TRUE,

ordered = c("Freq_now_B", "Freq_young_B", "NatureAppreciation_Now", "NatureAppreciation_Young", "Act_after_school_outdoors", "Childhood_memory",

"Extraverted_Enthusiastic", "Critical_quarrelsome", "Dependable_Selfdiscipline", "Anxious_easilyupset", "Opentonewex_complex", "Reserved_quiet", "Sympathetic_warm", "Disorganised_careless", "Calm_emotionallystable", "Conventional_uncreative",

"Limit", "Modify", "Interfere", "Ingenuity", "Abuse", "NatRes", "Rights", "Industrial", "Laws", "Crisis", "Spaceship", "Rule", "Balance", "Learn", "Eco_crsis",

"Male", "Single", "Housing_type"

))

There were 30 warnings (use warnings() to see them)

> warnings()

Warning messages:

1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

2: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, ... :

lavaan WARNING: could not invert information matrix

3: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

4: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

5: In lavaan::lavaan(model = "\n#measurement model \nsocioecon =~ Male + Age + Single + Singaporean + Chinese + NoReligion + Hokkien + HHincomeperpersonK + Housing_type\npersonality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative\nNEP=~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis\npastexposure =~ Freq_young_B + Act_after_school_outdoors + NatureAppreciation_Young + Childhood_memory \ncurrentbehav =~ NatureAppreciation_Now + Freq_now_B\n\n#regression \ncurrentbehav ~ NEP \nNEP ~ Instrumental + Relational + Intrinsic \nInstrumental ~ personality + pastexposure \nRelational ~ personality + pastexposure \nIntrinsic ~ personality + pastexposure \npersonality ~ socioecon + pastexposure\npastexposure ~ socioecon\n", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

6: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

7: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, ... :

lavaan WARNING: could not invert information matrix

8: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

9: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

10: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

11: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

12: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, ... :

lavaan WARNING: could not invert information matrix

13: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

14: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

15: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

16: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

17: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, ... :

lavaan WARNING: could not invert information matrix

18: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

19: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

20: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

21: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

22: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, ... :

lavaan WARNING: could not invert information matrix

23: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

24: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

25: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

26: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, ... :

lavaan WARNING:

Could not compute standard errors! The information matrix could

not be inverted. This may be a symptom that the model is not

identified.

27: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, ... :

lavaan WARNING: could not invert information matrix

28: In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative

29: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

30: In lavaan(slotOptions = structure(list(model.type = "sem", ... :

lavaan WARNING: not all elements of the gradient are (near) zero;

the optimizer may not have found a local solution;

use lavInspect(fit, "optim.gradient") to investigate

Also, it seems like standard errors are not computed

> summary(fit9)

Error in .local(object, ...) :

Standard errors could not be computed in any imputations, so it is not possible to calculate the within-imputation portion of sampling variance.

Here is my imputation code, I used method = "pmm" here. However, I also tried using method = "cart" because I have a mix of continuous and categorical variables in my data. Both methods of imputations seem to be give me similar output after introducing into sem.mi

fulldata_complete2 = select(fulldata, Male, Age, Singaporean, Chinese, Hokkien, NoReligion, Single, HHincomeperpersonK, Housing_type,

Extraverted_Enthusiastic, Critical_quarrelsome, Dependable_Selfdiscipline, Anxious_easilyupset, Opentonewex_complex, Reserved_quiet, Sympathetic_warm, Disorganised_careless, Calm_emotionallystable, Conventional_uncreative,

Act_after_school_outdoors, Childhood_memory, Freq_now_B, Freq_young_B, NatureAppreciation_Now, NatureAppreciation_Young, Freq_of_visit_nowConK, Freq_of_visit_youngConK,

Limit, Modify, Interfere, Ingenuity, Abuse, NatRes, Rights, Industrial, Laws, Crisis, Spaceship, Rule, Balance, Learn, Eco_crsis,

Instrumental, Relational, Intrinsic)

imputed_fulldata <- mice(fulldata_complete2, m =5, maxit = 50, method = "pmm", seed = "500")

summary(imputed_fulldata)

df1 = complete(imputed_fulldata,1)

df2 = complete(imputed_fulldata,2)

df3 = complete(imputed_fulldata,3)

df4 = complete(imputed_fulldata,4)

df5 = complete(imputed_fulldata,5)

mi_list <- list(df1, df2, df3, df4, df5)

sapply(mi_list, class)

Terrence Jorgensen

unread,

Mar 11, 2019, 5:24:05 AM3/11/19

to lavaan

I have changed the estimator to "WLSMV" but it seems that there are more warnings now.

Is your sample size at least 1000? Large samples are required for DWLS estimation, and for the subsequent robust corrections to work as expected. Your model is quite large, so the sample size will need to be very large as well.

Try fitting a CFA before a structural regression model. Also, try fitting pieces of your model (e.g.,

I also took out a few variables from socio-demo factors because they are not so important and changed freq_of_visit to a dummy coded variable

VBNlessSEmodel <-'
#measurement model
socioecon =~ Male + Age + Single + HHincomeperpersonK + Housing_type

socioecon is not a common factor. This model implies that raising socioecon by 1 unit would simultaneously affect respondents' sex, age, marital status, income, and housing type. SES is a famous example of a "formative construct", which you can search to find much literature about (or ask on SEMNET).

http://www2.gsu.edu/~mkteer/semnet.html

Modeling SES as a common factor might be causing some of your problems, which could be resolved by treating those socioeconomic indicators as independent indicators, or by modeling SES as a formative construct (which cannot be modeled unless SES predicts another outcome).

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

Sin Ching See

unread,

Mar 12, 2019, 1:52:03 AM3/12/19

to lavaan

Thanks for the reply!

My sample size is only 501, do you recommend me to keep using DWLS? I'm thinking of respecifying my model such that endogenous variables are all continuous so that I can use MLR as an estimator instead.

I ran CFA on my measurement model and it shows that there is no solution:

LVCFA2 <-'

#measurement model

socioecon =~ Male + Age + Singaporean + Chinese + NoReligion + Single + HHincomeperpersonK + Housing_type

personality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative

NEP=~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis

pastexposure =~ Freq_young_B + Act_after_school_outdoors + NatureAppreciation_Young + Childhood_memory

currentbehav =~ NatureAppreciation_Now + Freq_now_B

'

Lvfit2 <- cfa(LVCFA2, data = fulldata)

summary(Lvfit2)

fitmeasure(Lvfit2)

Warning message:

In lavaan::lavaan(model = LVCFA3, data = fulldata, model.type = "cfa", :

lavaan WARNING: the optimizer warns that a solution has NOT been found!

So I tried running a CFA on another measurement model, where I combined currentbehav with pastexposure (changing the number of latent variables to 4), and a solution can be reached

LVCFA <- '

#measurement model (latent variables)

socioecon =~ Male + Age + Singaporean + Chinese + Hokkien + NoReligion + Single + HHincomeperpersonK + Housing_type

personality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative

envtproness =~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis

pastexposure =~ Act_after_school_outdoors + Freq_young_B + NatureAppreciation_Young + Freq_now_B + NatureAppreciation_Now + Childhood_memory

'

lavaan 0.6-3 ended normally after 107 iterations

Optimization method NLMINB

Number of free parameters 86

Used Total

Number of observations 309 501

Estimator ML

Model Fit Test Statistic 1917.905

Degrees of freedom 734

P-value (Chi-square) 0.000

Model test baseline model:

Minimum Function Test Statistic 2730.281

Degrees of freedom 780

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.393

Tucker-Lewis Index (TLI) 0.355

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -15993.339

Loglikelihood unrestricted model (H1) -15034.387

Number of free parameters 86

Akaike (AIC) 32158.678

Bayesian (BIC) 32479.746

Sample-size adjusted Bayesian (BIC) 32206.988

Root Mean Square Error of Approximation:

RMSEA 0.072

90 Percent Confidence Interval 0.068 0.076

P-value RMSEA <= 0.05 0.000

Standardized Root Mean Square Residual:

SRMR 0.088

Parameter Estimates:

Information Expected

Information saturated (h1) model Structured

Standard Errors Standard

Latent Variables:

Estimate Std.Err z-value P(>|z|)

socioecon =~

Male 1.000

Age 2.715 1.122 2.420 0.016

Singaporean 0.035 0.040 0.862 0.389

Chinese 0.087 0.048 1.826 0.068

Hokkien 0.083 0.077 1.086 0.277

NoReligion 0.119 0.081 1.468 0.142

Single -0.027 0.060 -0.444 0.657

HHincomprprsnK 0.168 0.231 0.726 0.468

Housing_type 0.050 0.447 0.111 0.912

personality =~

Extrvrtd_Enths 1.000

Criticl_qrrlsm -0.362 0.171 -2.117 0.034

Dpndbl_Slfdscp 0.850 0.182 4.661 0.000

Anxious_slypst -0.730 0.194 -3.769 0.000

Opentnwx_cmplx 0.529 0.143 3.704 0.000

Reserved_quiet -0.715 0.191 -3.736 0.000

Sympathetc_wrm 0.530 0.145 3.654 0.000

Disrgnsd_crlss -0.670 0.191 -3.500 0.000

Clm_mtnllystbl 0.720 0.177 4.074 0.000

Convntnl_ncrtv -0.193 0.141 -1.370 0.171

envtproness =~

Limit 1.000

Modify -0.174 0.179 -0.973 0.331

Interfere 1.000 0.193 5.178 0.000

Ingenuity -0.025 0.177 -0.142 0.887

Abuse 1.317 0.197 6.696 0.000

NatRes 0.303 0.168 1.804 0.071

Rights 0.884 0.184 4.803 0.000

Industrial -0.499 0.210 -2.378 0.017

Laws 0.931 0.163 5.725 0.000

Crisis -0.533 0.197 -2.699 0.007

Spaceship 1.070 0.190 5.631 0.000

Rule -0.198 0.206 -0.960 0.337

Balance 0.826 0.161 5.118 0.000

Learn 0.068 0.171 0.398 0.691

Eco_crsis 1.445 0.212 6.812 0.000

pastexposure =~

Act_ftr_schl_t 1.000

Freq_young_B 1.236 0.195 6.340 0.000

NtrApprctn_Yng -0.065 0.086 -0.751 0.453

Freq_now_B 0.703 0.149 4.718 0.000

NatrApprctn_Nw 0.007 0.102 0.067 0.946

Childhood_mmry 2.241 0.375 5.981 0.000

Covariances:

Estimate Std.Err z-value P(>|z|)

socioecon ~~

personality 0.013 0.028 0.474 0.635

envtproness -0.015 0.013 -1.120 0.263

pastexposure -0.005 0.009 -0.516 0.606

personality ~~

envtproness -0.023 0.026 -0.869 0.385

pastexposure 0.113 0.027 4.107 0.000

envtproness ~~

pastexposure 0.011 0.009 1.271 0.204

Variances:

Estimate Std.Err z-value P(>|z|)

.Male 0.052 0.080 0.654 0.513

.Age 3.817 0.663 5.758 0.000

.Singaporean 0.071 0.006 12.419 0.000

.Chinese 0.062 0.005 12.300 0.000

.Hokkien 0.244 0.020 12.410 0.000

.NoReligion 0.232 0.019 12.379 0.000

.Single 0.175 0.014 12.427 0.000

.HHincomprprsnK 2.443 0.197 12.423 0.000

.Housing_type 9.807 0.789 12.430 0.000

.Extrvrtd_Enths 2.221 0.212 10.500 0.000

.Criticl_qrrlsm 2.716 0.222 12.225 0.000

.Dpndbl_Slfdscp 1.333 0.132 10.104 0.000

.Anxious_slypst 2.412 0.210 11.488 0.000

.Opentnwx_cmplx 1.339 0.116 11.540 0.000

.Reserved_quiet 2.381 0.207 11.515 0.000

.Sympathetc_wrm 1.407 0.122 11.578 0.000

.Disrgnsd_crlss 2.569 0.220 11.686 0.000

.Clm_mtnllystbl 1.780 0.159 11.186 0.000

.Convntnl_ncrtv 1.979 0.160 12.350 0.000

.Limit 0.743 0.063 11.764 0.000

.Modify 1.319 0.106 12.419 0.000

.Interfere 0.793 0.067 11.806 0.000

.Ingenuity 1.316 0.106 12.430 0.000

.Abuse 0.258 0.029 8.921 0.000

.NatRes 1.115 0.090 12.389 0.000

.Rights 0.818 0.068 11.959 0.000

.Industrial 1.657 0.134 12.356 0.000

.Laws 0.439 0.038 11.446 0.000

.Crisis 1.418 0.115 12.332 0.000

.Spaceship 0.629 0.055 11.525 0.000

.Rule 1.758 0.142 12.419 0.000

.Balance 0.566 0.048 11.834 0.000

.Learn 1.231 0.099 12.428 0.000

.Eco_crsis 0.219 0.029 7.563 0.000

.Act_ftr_schl_t 0.150 0.016 9.647 0.000

.Freq_young_B 0.129 0.017 7.539 0.000

.NtrApprctn_Yng 0.100 0.008 12.413 0.000

.Freq_now_B 0.199 0.017 11.429 0.000

.NatrApprctn_Nw 0.142 0.011 12.430 0.000

.Childhood_mmry 0.805 0.082 9.838 0.000

socioecon 0.197 0.082 2.402 0.016

personality 0.552 0.175 3.152 0.002

envtproness 0.168 0.047 3.570 0.000

pastexposure 0.066 0.016 4.136 0.000

I also ran a CFA without the socioeconomic factor, considering how it shouldn't really be considered a latent variable

LVCFA3 <-'

personality =~ Extraverted_Enthusiastic + Critical_quarrelsome + Dependable_Selfdiscipline + Anxious_easilyupset + Opentonewex_complex + Reserved_quiet + Sympathetic_warm + Disorganised_careless + Calm_emotionallystable + Conventional_uncreative

NEP=~ Limit + Modify + Interfere + Ingenuity + Abuse + NatRes + Rights + Industrial + Laws + Crisis + Spaceship + Rule + Balance + Learn + Eco_crsis

pastexposure =~ Freq_young_B + Act_after_school_outdoors + NatureAppreciation_Young + Childhood_memory

currentbehav =~ NatureAppreciation_Now + Freq_now_B'

Lvfit3 <- cfa(LVCFA3, data = fulldata)

There was a warning message, but a solution was reached too

Warning message:

In lav_object_post_check(object) :

lavaan WARNING: covariance matrix of latent variables

is not positive definite;

use lavInspect(fit, "cov.lv") to investigate.

lavaan 0.6-3 ended normally after 100 iterations

Optimization method NLMINB

Number of free parameters 68

Used Total

Number of observations 494 501

Estimator ML

Model Fit Test Statistic 1908.862

Degrees of freedom 428

P-value (Chi-square) 0.000

Model test baseline model:

Minimum Function Test Statistic 3129.332

Degrees of freedom 465

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.444

Tucker-Lewis Index (TLI) 0.396

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -20853.089

Loglikelihood unrestricted model (H1) -19898.658

Number of free parameters 68

Akaike (AIC) 41842.178

Bayesian (BIC) 42127.950

Sample-size adjusted Bayesian (BIC) 41912.117

Root Mean Square Error of Approximation:

RMSEA 0.084

90 Percent Confidence Interval 0.080 0.088

P-value RMSEA <= 0.05 0.000

Standardized Root Mean Square Residual:

SRMR 0.091

Parameter Estimates:

Information Expected

Information saturated (h1) model Structured

Standard Errors Standard

Latent Variables:

Estimate Std.Err z-value P(>|z|)

personality =~

Extrvrtd_Enths 1.000

Criticl_qrrlsm -0.207 0.118 -1.752 0.080

Dpndbl_Slfdscp 0.872 0.136 6.405 0.000

Anxious_slypst -0.563 0.133 -4.234 0.000

Opentnwx_cmplx 0.607 0.108 5.611 0.000

Reserved_quiet -0.618 0.132 -4.688 0.000

Sympathetc_wrm 0.558 0.108 5.175 0.000

Disrgnsd_crlss -0.688 0.139 -4.951 0.000

Clm_mtnllystbl 0.666 0.123 5.437 0.000

Convntnl_ncrtv -0.183 0.103 -1.778 0.075

NEP =~

Limit 1.000

Modify -0.338 0.121 -2.780 0.005

Interfere 0.945 0.122 7.762 0.000

Ingenuity -0.272 0.120 -2.271 0.023

Abuse 1.144 0.115 9.914 0.000

NatRes 0.117 0.111 1.050 0.294

Rights 0.731 0.112 6.531 0.000

Industrial -0.545 0.138 -3.945 0.000

Laws 0.735 0.094 7.795 0.000

Crisis -0.788 0.136 -5.798 0.000

Spaceship 0.839 0.112 7.473 0.000

Rule -0.478 0.141 -3.383 0.001

Balance 0.761 0.104 7.327 0.000

Learn -0.186 0.117 -1.591 0.112

Eco_crsis 1.319 0.128 10.316 0.000

pastexposure =~

Freq_young_B 1.000

Act_ftr_schl_t 0.816 0.114 7.167 0.000

NtrApprctn_Yng 0.022 0.056 0.395 0.693

Childhood_mmry 1.830 0.251 7.294 0.000

currentbehav =~

NatrApprctn_Nw 1.000

Freq_now_B 3.874 1.702 2.276 0.023

Covariances:

Estimate Std.Err z-value P(>|z|)

personality ~~

NEP -0.013 0.024 -0.525 0.600

pastexposure 0.114 0.023 4.891 0.000

currentbehav 0.023 0.011 2.083 0.037

NEP ~~

pastexposure 0.014 0.010 1.492 0.136

currentbehav 0.006 0.004 1.587 0.113

pastexposure ~~

currentbehav 0.015 0.007 2.318 0.020

Variances:

Estimate Std.Err z-value P(>|z|)

.Extrvrtd_Enths 2.111 0.163 12.926 0.000

.Criticl_qrrlsm 2.564 0.164 15.619 0.000

.Dpndbl_Slfdscp 1.276 0.105 12.202 0.000

.Anxious_slypst 2.512 0.168 14.981 0.000

.Opentnwx_cmplx 1.193 0.086 13.904 0.000

.Reserved_quiet 2.266 0.154 14.732 0.000

.Sympathetc_wrm 1.353 0.094 14.368 0.000

.Disrgnsd_crlss 2.377 0.163 14.551 0.000

.Clm_mtnllystbl 1.620 0.115 14.110 0.000

.Convntnl_ncrtv 1.958 0.125 15.616 0.000

.Limit 0.648 0.045 14.419 0.000

.Modify 1.284 0.082 15.643 0.000

.Interfere 0.750 0.051 14.719 0.000

.Ingenuity 1.270 0.081 15.668 0.000

.Abuse 0.306 0.026 12.000 0.000

.NatRes 1.138 0.072 15.706 0.000

.Rights 0.787 0.052 15.151 0.000

.Industrial 1.555 0.100 15.558 0.000

.Laws 0.447 0.030 14.703 0.000

.Crisis 1.276 0.083 15.312 0.000

.Spaceship 0.676 0.046 14.846 0.000

.Rule 1.683 0.108 15.604 0.000

.Balance 0.595 0.040 14.903 0.000

.Learn 1.233 0.079 15.693 0.000

.Eco_crsis 0.247 0.025 9.725 0.000

.Freq_young_B 0.137 0.014 9.550 0.000

.Act_ftr_schl_t 0.169 0.014 12.409 0.000

.NtrApprctn_Yng 0.093 0.006 15.712 0.000

.Childhood_mmry 0.756 0.063 11.963 0.000

.NatrApprctn_Nw 0.150 0.010 15.363 0.000

.Freq_now_B 0.216 0.034 6.376 0.000

personality 0.622 0.144 4.311 0.000

NEP 0.230 0.042 5.510 0.000

pastexposure 0.092 0.016 5.631 0.000

currentbehav 0.001 0.002 0.496 0.620

lavInspect(Lvfit3, "cov.lv")

prsnlt NEP pstxps crrntb

personality 0.622

NEP -0.013 0.230

pastexposure 0.114 0.014 0.092

currentbehav 0.023 0.006 0.015 0.001

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