Multigroup Analysis with binary outcome, equal constraints problem

Chong Man Chow

unread,

Jun 5, 2023, 10:53:19 AM6/5/23

to lavaan

Dear All

I ran into an obstacle when trying to estimate a path model with binary outcome. In the model below, I have the DV gun_purchase as a binary outcome variable, and I have used the DWLS estimator. The model is estimated for White, NonWhiteMinority, and Asian groups (3 groups analysis). It was found that the variance for White in the DV gun_purchase is negative. Trying to tackle the negative variance issue, I tried to constrain the variance for the variable to be equal across 3 groups with

'gun_purchase ~~ c(v1,v1,v1)*gun_purchase' but it would not do the job (the variances still came up to be different, and one of them is negative).

I also have tried to fix the negative variance for the first group to be 0 by using

'gun_purchase ~~ c(0,v2,v2)*gun_purchase' . But again, the line won't work.

Any suggestions on how to handle this issue would be much appreciated.

gun_purchase.model1 <-
+ '
+
+ #covariates
+ gun_purchase ~ gendergrp + agegrp_31_50 + agegrp_51_64 + agegrp_65_Older + maritalstatusgrp_married + incomegrp_35000_49999 +
+ incomegrp_50000_74999 + incomegrp_75000_99999 + incomegrp_100000_more + educationgrp_some_college + educationgrp_college_graduate_above
+
+
+ scovid_antic_discr ~ gendergrp + agegrp_31_50 + agegrp_51_64 + agegrp_65_Older + maritalstatusgrp_married + incomegrp_35000_49999 +
+ incomegrp_50000_74999 + incomegrp_75000_99999 + incomegrp_100000_more + educationgrp_some_college + educationgrp_college_graduate_above
+
+ mentalhealth ~ gendergrp + agegrp_31_50 + agegrp_51_64 + agegrp_65_Older + maritalstatusgrp_married + incomegrp_35000_49999 +
+ incomegrp_50000_74999 + incomegrp_75000_99999 + incomegrp_100000_more + educationgrp_some_college + educationgrp_college_graduate_above
+
+ alcohol ~ gendergrp + agegrp_31_50 + agegrp_51_64 + agegrp_65_Older + maritalstatusgrp_married + incomegrp_35000_49999 +
+ incomegrp_50000_74999 + incomegrp_75000_99999 + incomegrp_100000_more + educationgrp_some_college + educationgrp_college_graduate_above
+
+
+ #Main model
+ gun_purchase ~ c(p6.0, p6.1, p6.2)*mentalhealth + c(p4.0, p4.1, p4.2)*scovid_antic_discr + c(p5.0, p5.1, p5.2)*alcohol
+
+ alcohol ~ c(p2.0, p2.1, p2.2)*scovid_antic_discr + c(p3.0, p3.1, p3.2)*mentalhealth
+
+ mentalhealth ~ c(p1.0, p1.1, p1.2)*scovid_antic_discr
+
+
+ gun_purchase ~~ c(v1, v2, v3)*gun_purchase
+
+ '
> gun_purchase.model1.fit <- sem(gun_purchase.model1, data = df, estimator="DWLS", group = "racegrp1")
Warning: lavaan WARNING: group variable ‘racegrp1’ contains missing values
Warning: lavaan WARNING: correlation between variables mentalhealth and gun_purchase is (nearly) 1.0Warning: lavaan WARNING: trouble constructing W matrix; used generalized inverse for A11 submatrixWarning: 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.Warning: lavaan WARNING: some estimated ov variances are negative
> summary(gun_purchase.model1.fit, fit.measures=TRUE)
lavaan 0.6-11.1676 ended normally after 352 iterations

Estimator DWLS
Optimization method NLMINB
Number of model parameters 174

Number of observations per group: Used Total
White 198 253
NonAsianMinority 208 268
Asian 823 916

Model Test User Model:

Test statistic NA
Degrees of freedom -3
P-value (Unknown) NA
Test statistic for each group:
White NA
NonAsianMinority NA
Asian NA

User Model versus Baseline Model:

Comparative Fit Index (CFI) NA
Tucker-Lewis Index (TLI) NA

Root Mean Square Error of Approximation:

RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA
P-value RMSEA <= 0.05 NA

Standardized Root Mean Square Residual:

SRMR 0.000

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Unstructured

Group 1 [White]:

Regressions:
Estimate Std.Err z-value P(>|z|)
gun_purchase ~
gndrgrp 0.194 NA
a_31_50 -0.264 NA
a_51_64 0.671 NA
ag_65_O 0.026 NA
mrtlst_ -0.017 NA
i_35000 0.764 NA
i_50000 0.311 NA
i_75000 0.114 NA
i_10000 0.521 NA
edctn__ 4.869 NA
edct___ 5.261 NA
scovid_antic_discr ~
gndrgrp 0.555 NA
a_31_50 -0.247 NA
a_51_64 -0.635 NA
ag_65_O -1.034 NA
mrtlst_ -0.017 NA
i_35000 -0.205 NA
i_50000 0.100 NA
i_75000 0.066 NA
i_10000 -0.013 NA
edctn__ 0.108 NA
edct___ 0.200 NA
mentalhealth ~
gndrgrp -0.165 NA
a_31_50 -0.033 NA
a_51_64 -0.357 NA
ag_65_O -0.545 NA
mrtlst_ 0.049 NA
i_35000 -0.490 NA
i_50000 -0.160 NA
i_75000 -0.359 NA
i_10000 -0.441 NA
edctn__ -0.007 NA
edct___ 0.122 NA
alcohol ~
gndrgrp 0.219 NA
a_31_50 -0.286 NA
a_51_64 -0.923 NA
ag_65_O -1.088 NA
mrtlst_ -0.609 NA
i_35000 -0.287 NA
i_50000 0.121 NA
i_75000 -0.006 NA
i_10000 0.598 NA
edctn__ 0.764 NA
edct___ 0.761 NA
gun_purchase ~
mntlhlt (p6.0) 1.240 NA
scvd_n_ (p4.0) -0.214 NA
alcohol (p5.0) 0.140 NA
alcohol ~
scvd_n_ (p2.0) 0.435 NA
mntlhlt (p3.0) -0.023 NA
mentalhealth ~
scvd_n_ (p1.0) 0.346 NA

Intercepts:
Estimate Std.Err z-value P(>|z|)
.gun_purchase 0.000
.scovd_ntc_dscr 1.105 NA
.mentalhealth 1.833 NA
.alcohol 2.749 NA

Thresholds:
Estimate Std.Err z-value P(>|z|)
gun_purchas|t1 9.463 NA

Variances:
Estimate Std.Err z-value P(>|z|)
.gun_prchs (v1) -0.064 NA
.scvd_ntc_ 0.922 NA
.mentlhlth 0.609 NA
.alcohol 3.209 NA

Scales y*:
Estimate Std.Err z-value P(>|z|)
gun_purchase 1.000

Group 2 [NonAsianMinority]:

Regressions:
Estimate Std.Err z-value P(>|z|)
gun_purchase ~
gndrgrp 0.293 NA
a_31_50 -0.513 NA
a_51_64 -0.232 NA
ag_65_O -0.614 NA
mrtlst_ -0.542 NA
i_35000 0.001 NA
i_50000 0.530 NA
i_75000 0.459 NA
i_10000 0.239 NA
edctn__ -0.132 NA
edct___ -0.031 NA
scovid_antic_discr ~
gndrgrp 0.038 NA
a_31_50 -0.225 NA
a_51_64 -0.849 NA
ag_65_O -0.951 NA
mrtlst_ -0.355 NA
i_35000 0.047 NA
i_50000 -0.490 NA
i_75000 0.156 NA
i_10000 -0.409 NA
edctn__ -0.022 NA
edct___ -0.035 NA
mentalhealth ~
gndrgrp 0.013 NA
a_31_50 -0.496 NA
a_51_64 -0.630 NA
ag_65_O -0.880 NA
mrtlst_ -0.324 NA
i_35000 -0.035 NA
i_50000 -0.165 NA
i_75000 -0.459 NA
i_10000 -0.409 NA
edctn__ -0.021 NA
edct___ -0.133 NA
alcohol ~
gndrgrp 0.047 NA
a_31_50 0.506 NA
a_51_64 0.109 NA
ag_65_O -0.229 NA
mrtlst_ -0.572 NA
i_35000 0.335 NA
i_50000 0.928 NA
i_75000 0.221 NA
i_10000 0.511 NA
edctn__ -0.116 NA
edct___ -0.085 NA
gun_purchase ~
mntlhlt (p6.1) 0.164 NA
scvd_n_ (p4.1) 0.342 NA
alcohol (p5.1) -0.075 NA
alcohol ~
scvd_n_ (p2.1) 0.395 NA
mntlhlt (p3.1) 0.174 NA
mentalhealth ~
scvd_n_ (p1.1) 0.320 NA

Intercepts:
Estimate Std.Err z-value P(>|z|)
.gun_purchase 0.000
.scovd_ntc_dscr 3.077 NA
.mentalhealth 2.335 NA
.alcohol 2.692 NA

Thresholds:
Estimate Std.Err z-value P(>|z|)
gun_purchas|t1 1.141 NA

Variances:
Estimate Std.Err z-value P(>|z|)
.gun_prchs (v2) 0.788 NA
.scvd_ntc_ 1.377 NA
.mentlhlth 0.520 NA
.alcohol 3.766 NA

Scales y*:
Estimate Std.Err z-value P(>|z|)
gun_purchase 1.000

Group 3 [Asian]:

Regressions:
Estimate Std.Err z-value P(>|z|)
gun_purchase ~
gndrgrp 0.366 NA
a_31_50 -0.299 NA
a_51_64 -0.993 NA
ag_65_O -0.696 NA
mrtlst_ -0.467 NA
i_35000 0.430 NA
i_50000 0.286 NA
i_75000 0.102 NA
i_10000 0.339 NA
edctn__ -0.098 NA
edct___ 0.087 NA
scovid_antic_discr ~
gndrgrp -0.013 NA
a_31_50 -0.338 NA
a_51_64 -0.866 NA
ag_65_O -0.772 NA
mrtlst_ -0.124 NA
i_35000 -0.182 NA
i_50000 -0.166 NA
i_75000 -0.085 NA
i_10000 -0.060 NA
edctn__ 0.058 NA
edct___ 0.010 NA
mentalhealth ~
gndrgrp -0.089 NA
a_31_50 -0.285 NA
a_51_64 -0.418 NA
ag_65_O -0.644 NA
mrtlst_ -0.058 NA
i_35000 0.064 NA
i_50000 0.041 NA
i_75000 -0.054 NA
i_10000 -0.126 NA
edctn__ -0.167 NA
edct___ -0.202 NA
alcohol ~
gndrgrp 0.355 NA
a_31_50 0.327 NA
a_51_64 -0.089 NA
ag_65_O -0.128 NA
mrtlst_ -0.234 NA
i_35000 0.200 NA
i_50000 0.320 NA
i_75000 0.401 NA
i_10000 0.602 NA
edctn__ 0.134 NA
edct___ 0.325 NA
gun_purchase ~
mntlhlt (p6.2) 0.150 NA
scvd_n_ (p4.2) 0.184 NA
alcohol (p5.2) 0.113 NA
alcohol ~
scvd_n_ (p2.2) 0.273 NA
mntlhlt (p3.2) 0.305 NA
mentalhealth ~
scvd_n_ (p1.2) 0.246 NA

Intercepts:
Estimate Std.Err z-value P(>|z|)
.gun_purchase 0.000
.scovd_ntc_dscr 2.373 NA
.mentalhealth 1.900 NA
.alcohol 0.808 NA

Thresholds:
Estimate Std.Err z-value P(>|z|)
gun_purchas|t1 2.244 NA

Variances:
Estimate Std.Err z-value P(>|z|)
.gun_prchs (v3) 0.880 NA
.scvd_ntc_ 0.985 NA
.mentlhlth 0.465 NA
.alcohol 2.983 NA

Scales y*:
Estimate Std.Err z-value P(>|z|)
gun_purchase 1.000

Terrence Jorgensen

unread,

Jun 12, 2023, 9:35:35 AM6/12/23

to lavaan

There are a few issues here.

I tried to constrain the variance for the variable to be equal across 3 groups with
'gun_purchase ~~ c(v1,v1,v1)*gun_purchase'

Residual variances are not model parameters under the default parameterization="delta". Even if you change to parameterization="theta", those parameters are fixed to 1 for identification, so they would already be equal.

http://www.statmodel.com/download/webnotes/CatMGLong.pdf

I also have tried to fix the negative variance for the first group to be 0 by using
'gun_purchase ~~ c(0,v2,v2)*gun_purchase' . But again, the line won't work.

Here, you are mixing labels (character strings) with numerical values (for fixing/freeing parameters). Those have to be specified separately.

gun_purchase ~~ c(0, NA, NA)*gun_purchase + c(v1, v2, v2)*gun_purchase

But this still won't run because your latent-response scale (which you could interpret as "propensity to purchase a gun", assumed normally distributed) is not identified.

The biggest problem you have is that the slopes are NOT COMPARABLE across groups. The latent response scale is set in each group using an arbitrary identification constraint, so the "units" are not the same. The way to link latent (locations and) scales across groups is to constrain thresholds to equality, but that requires 2 thresholds (1 to identify the intercept, 1 to identify the marginal or residual variance). Binary data have only 1 threshold, so group differences in variance are completely confounded with group differences in intercepts.

Paul Allison and others (e.g., Breen) have brought up this issue before, sometimes in the context of logistic regression (same issue, if you believe in the latent-response interpretation).

Any suggestions on how to handle this issue would be much appreciated.

Running a single-group model with dummy/contrast codes for groups would side-step the issue, although the same assumption is merely implicit (and the residual variance would be equal by definition, under either parameterization, perhaps avoiding the negative one). The moderation by group would have to represented the OLS regression way, by calculating product terms and testing them.

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

Chong Man Chow

unread,

Jun 12, 2023, 10:31:18 AM6/12/23

to lav...@googlegroups.com

Hi Terrence

Thank you so much for the detailed response. They are very helpful. I will try to come up with an alternative strategy to deal with the data.

Thanks,
Chong.

--
You received this message because you are subscribed to a topic in the Google Groups "lavaan" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/lavaan/6c7pr1q8aHE/unsubscribe.
To unsubscribe from this group and all its topics, send an email to lavaan+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/e88f06b7-ba61-422a-9473-6dda7661f425n%40googlegroups.com.

Reply all

Reply to author

Forward