Running RI-CLPM with semTools auxiliary: residuals of the observed variables (theta) is not positive definite;

Atanas Janackovski

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Sep 15, 2021, 6:04:15 PM9/15/21

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I am running an RI-CLPM and using the semTools::auxilary function with additional covariates to help model estimate the missing data under MAR and FIML estimation. However, I am getting the error: 'residuals of the observed variables (theta) is not positive definite'. This seems to be in one of the covariates / auxiliary variables. See below for specification and relevant output.

Can someone please give guidance on where I should go with this error? I have listed the categorical variables and also tried to apply the "theta" parameterization, but still getting this warning.

Thanks in advance.

--------

aux_vars <-
c("ac_1", "age", "sex_mf", "cov_sess", "hxdsh", "hxtrauma")

riclpm_sat_aux2 <-
lavaan.auxiliary(
    riclpm_sat_mod,
    aux = aux_vars,
    data = phd_fin_wide,
    missing = "ML",
    estimator = "MLR",
    meanstructure = TRUE,
    int.ov.free = TRUE,
    bounds = TRUE,
    ordered = c("sex_mf", "hxdsh", "hxtrauma"),
    parameterization = "theta"
)

> lavInspect(riclpm_sat_aux2, "post.check")

[1] FALSE
Warning message:
In lav_object_post_check(object) :
lavaan WARNING: the covariance matrix of the residuals of the observed
                variables (theta) is not positive definite;
                use lavInspect(fit, "theta") to investigate.
> lavInspect(riclpm_sat_aux2, "theta")
         pb_1   pb_2   pb_3   pb_4   pb_5   tb_1   tb_2   tb_3   tb_4   tb_5   bhs_1 bhs_2 bhs_3 bhs_4 bhs_5 dep_1 dep_2 dep_3 dep_4 dep_5 si_1   si_2   si_3   si_4   si_5   ac_1   age    sex_mf cv_sss hxdsh hxtram
pb_1      0.000
pb_2      0.000 0.000
pb_3      0.000 0.000 0.000
pb_4      0.000 0.000 0.000 0.000
pb_5      0.000 0.000 0.000 0.000 0.000
tb_1      0.000 0.000 0.000 0.000 0.000 0.000
tb_2      0.000 0.000 0.000 0.000 0.000 0.000 0.000
tb_3      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
tb_4      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
tb_5      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
bhs_1     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
bhs_2     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
bhs_3     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
bhs_4     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
bhs_5     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
dep_1     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
dep_2     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
dep_3     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
dep_4     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
dep_5     0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
si_1      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
si_2      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
si_3      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
si_4      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
si_5      0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
ac_1     14.747 16.279 12.361 14.449 13.089 9.364 9.006 6.567 8.525 8.432 9.392 10.200 8.585 7.948 8.907 6.616 8.404 5.743 7.499 7.774 13.082 8.643 5.289 5.998 8.525 41.959
age      -1.304 -2.489 -1.267 -1.636 -2.268 3.423 2.247 3.681 3.132 1.024 -0.028 0.200 0.287 -0.154 0.220 1.607 0.941 1.922 1.999 1.137 1.803 1.258 1.179 1.444 -0.046 -1.891 8.975
sex_mf   -0.537 -0.525 -0.490 -0.565 -0.684 -0.185 -0.325 -0.216 -0.385 -0.567 -0.133 -0.070 -0.110 -0.120 -0.274 -0.078 -0.118 -0.159 -0.228 -0.302 -0.148 0.062 0.282 -0.111 -0.191 0.079 0.282 0.206
cov_sess 1.148 3.324 5.754 7.513 8.249 1.425 3.602 4.442 6.465 6.608 1.460 2.255 3.106 3.603 4.581 0.941 2.018 2.907 4.138 4.950 2.290 3.347 3.939 5.005 4.208 0.987 -0.740 -0.097 4.651
hxdsh     0.948 0.706 0.447 0.630 0.571 0.722 0.870 0.984 0.977 0.920 0.342 0.339 0.374 0.348 0.532 0.306 0.260 0.262 0.431 0.445 0.534 0.345 0.101 0.329 0.149 0.376 0.104 -0.050 -0.003 0.208
hxtrauma 0.585 0.520 0.590 0.470 0.388 0.380 0.336 0.539 0.500 0.309 0.146 0.080 0.257 0.065 0.132 0.227 0.211 0.370 0.252 0.233 0.228 0.533 0.361 0.562 0.212 0.194 0.144 -0.035 -0.045 0.072 0.246
>

Ulrich Schroeders

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Sep 16, 2021, 2:46:02 AM9/16/21

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Dear Atanas,

1. You have to add fixed.x = FALSE (see ?auxiliary).

2. Auxiliary can't be ordered.

I'm not sure if this tackles your model issues.

Kind regards

Ulrich

Atanas Janackovski

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Sep 17, 2021, 8:11:16 AM9/17/21

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Thanks Ulrich… Always read the docs!

However, this did not solve my problem. I found a post with a similar issues here: https://groups.google.com/g/lavaan/c/ihYCsLW5528

Terrence Jorgensen wrote in the linked post: "… your theta matrix is NPD because it is impossible for two variables (here, "residuals" … to covary (i.e., to vary together) when they don't even vary." I am new to SEM so do not fully understand what is happening, but I've posted my model syntax as well as the warning. Sorry for all the syntax and output. I think maybe this is because I've contrained the observed varaibles and latent variables (e.g., '1*pb_1). I followed the model syntax from Mulder and Hamaker (2021).

Any suggestions if I need to do anything to correct this?

Mulder, J. D., & Hamaker, E. L. (2021). Three Extensions of the Random Intercept Cross-Lagged Panel Model. Structural Equation Modeling: A Multidisciplinary Journal, 28(4), 638–648. doi: 10/ghjkz9

riclpm_sat_mod <- '
## Create between components (random intercepts)
RIpb =~ 1*pb_1 + 1*pb_2 + 1*pb_3 + 1*pb_4 + 1*pb_5
RItb =~ 1*tb_1 + 1*tb_2 + 1*tb_3 + 1*tb_4 + 1*tb_5
RIbhs =~ 1*bhs_1 + 1*bhs_2 + 1*bhs_3 + 1*bhs_4 + 1*bhs_5
RIdep =~ 1*dep_1 + 1*dep_2 + 1*dep_3 + 1*dep_4 + 1*dep_5
RIsi =~ 1*si_1 + 1*si_2 + 1*si_3 + 1*si_4 + 1*si_5
## =======
## Create within-person centered variables
wpb_1 =~ 1*pb_1
wpb_2 =~ 1*pb_2
wpb_3 =~ 1*pb_3
wpb_4 =~ 1*pb_4
wpb_5 =~ 1*pb_5
## ==
wtb_1 =~ 1*tb_1
wtb_2 =~ 1*tb_2
wtb_3 =~ 1*tb_3
wtb_4 =~ 1*tb_4
wtb_5 =~ 1*tb_5
## ==
wbhs_1 =~ 1*bhs_1
wbhs_2 =~ 1*bhs_2
wbhs_3 =~ 1*bhs_3
wbhs_4 =~ 1*bhs_4
wbhs_5 =~ 1*bhs_5
## ==
wdep_1 =~ 1*dep_1
wdep_2 =~ 1*dep_2
wdep_3 =~ 1*dep_3
wdep_4 =~ 1*dep_4
wdep_5 =~ 1*dep_5
## ==
wsi_1 =~ 1*si_1
wsi_2 =~ 1*si_2
wsi_3 =~ 1*si_3
wsi_4 =~ 1*si_4
wsi_5 =~ 1*si_5
## =====
##
## Estimate the lagged effects between the within-person centered variables.
wpb_2 + wtb_2 + wbhs_2 + wdep_2 + wsi_2 ~ wpb_1 + wtb_1 + wbhs_1 + wdep_1 + wsi_1 # nolint
wpb_3 + wtb_3 + wbhs_3 + wdep_3 + wsi_3 ~ wpb_2 + wtb_2 + wbhs_2 + wdep_2 + wsi_2 # nolint
wpb_4 + wtb_4 + wbhs_4 + wdep_4 + wsi_4 ~ wpb_3 + wtb_3 + wbhs_3 + wdep_3 + wsi_3 # nolint
wpb_5 + wtb_5 + wbhs_5 + wdep_5 + wsi_5 ~ wpb_4 + wtb_4 + wbhs_4 + wdep_4 + wsi_4 # nolint
## ==
## Estimate the covariance between the within-person centered variables
## at the first wave.
wpb_1 ~~ wtb_1 # Covariance
wpb_1 ~~ wbhs_1
wpb_1 ~~ wdep_1
wpb_1 ~~ wsi_1
wtb_1 ~~ wbhs_1
wtb_1 ~~ wdep_1
wtb_1 ~~ wsi_1
wbhs_1 ~~ wsi_1
wbhs_1 ~~ wdep_1
wdep_1 ~~ wsi_1
## Estimate the covariances between the residuals of the within-person
## centered variables (the innovations).
## time_2
wpb_2 ~~ wtb_2
wpb_2 ~~ wbhs_2
wpb_2 ~~ wdep_2
wpb_2 ~~ wsi_2
wtb_2 ~~ wbhs_2
wtb_2 ~~ wdep_2
wtb_2 ~~ wsi_2
wbhs_2 ~~ wsi_2
wbhs_2 ~~ wdep_2
wdep_2 ~~ wsi_2
## time_3
wpb_3 ~~ wtb_3
wpb_3 ~~ wbhs_3
wpb_3 ~~ wdep_3
wpb_3 ~~ wsi_3
wtb_3 ~~ wbhs_3
wtb_3 ~~ wdep_3
wtb_3 ~~ wsi_3
wbhs_3 ~~ wsi_3
wbhs_3 ~~ wdep_3
wdep_3 ~~ wsi_3
## time_4
wpb_4 ~~ wtb_4
wpb_4 ~~ wbhs_4
wpb_4 ~~ wdep_4
wpb_4 ~~ wsi_4
wtb_4 ~~ wbhs_4
wtb_4 ~~ wdep_4
wtb_4 ~~ wsi_4
wbhs_4 ~~ wsi_4
wbhs_4 ~~ wdep_4
wdep_4 ~~ wsi_4
## time_5
wpb_5 ~~ wtb_5
wpb_5 ~~ wbhs_5
wpb_5 ~~ wdep_5
wpb_5 ~~ wsi_5
wtb_5 ~~ wbhs_5
wtb_5 ~~ wdep_5
wtb_5 ~~ wsi_5
wbhs_5 ~~ wsi_5
wbhs_5 ~~ wdep_5
wdep_5 ~~ wsi_5
## Estimate the variance and covariance of the random intercepts.
RIpb ~~ RIpb
RItb ~~ RItb
RIbhs ~~ RIbhs
RIdep ~~ RIdep
RIsi ~~ RIsi
## ==
RIpb ~~ RItb
RIpb ~~ RIbhs
RIpb ~~ RIdep
RIpb ~~ RIsi
RItb ~~ RIbhs
RItb ~~ RIdep
RItb ~~ RIsi
RIbhs ~~ RIsi
RIbhs ~~ RIdep
RIdep ~~ RIsi
## Estimate the (residual) variance of the within-person centered variables.
wpb_1 ~~ wpb_1 # Variances
wtb_1 ~~ wtb_1
wbhs_1 ~~ wbhs_1
wdep_1 ~~ wdep_1
wsi_1 ~~ wsi_1
## time_2
wpb_2 ~~ wpb_2 # Residual variances
wtb_2 ~~ wtb_2
wbhs_2 ~~ wbhs_2
wdep_2 ~~ wdep_2
wsi_2 ~~ wsi_2
## time_3
wpb_3 ~~ wpb_3 # Residual variances
wtb_3 ~~ wtb_3
wbhs_3 ~~ wbhs_3
wdep_3 ~~ wdep_3
wsi_3 ~~ wsi_3
## time_4
wpb_4 ~~ wpb_4 # Residual variances
wtb_4 ~~ wtb_4
wbhs_4 ~~ wbhs_4
wdep_4 ~~ wdep_4
wsi_4 ~~ wsi_4
## time_5
wpb_5 ~~ wpb_5 # Residual variances
wtb_5 ~~ wtb_5
wbhs_5 ~~ wbhs_5
wdep_5 ~~ wdep_5
wsi_5 ~~ wsi_5
'

> lavInspect(riclpm_sat_aux, "theta")

pb_1 pb_2 pb_3 pb_4 pb_5 tb_1 tb_2 tb_3 tb_4 tb_5 bhs_1 bhs_2 bhs_3 bhs_4 bhs_5 dep_1 dep_2 dep_3 dep_4 dep_5 si_1

pb_1 0.000

pb_2 0.000 0.000

pb_3 0.000 0.000 0.000

pb_4 0.000 0.000 0.000 0.000

pb_5 0.000 0.000 0.000 0.000 0.000

tb_1 0.000 0.000 0.000 0.000 0.000 0.000

tb_2 0.000 0.000 0.000 0.000 0.000 0.000 0.000

tb_3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

tb_4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

tb_5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

bhs_1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

bhs_2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

bhs_3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

bhs_4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

bhs_5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

dep_1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

dep_2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

dep_3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

dep_4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

dep_5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

si_1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

si_2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

si_3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

si_4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

si_5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

ac_1 14.756 16.274 12.363 14.434 13.135 9.362 9.022 6.540 8.538 8.422 9.382 10.205 8.572 7.904 8.885 6.595 8.409 5.737 7.483 7.713 13.041

age -1.332 -2.501 -1.277 -1.690 -2.253 3.389 2.252 3.679 3.097 0.922 -0.044 0.203 0.298 -0.247 0.102 1.607 0.946 1.905 1.989 1.048 1.842

sex_mf -0.540 -0.524 -0.489 -0.566 -0.672 -0.182 -0.332 -0.218 -0.388 -0.572 -0.134 -0.073 -0.111 -0.117 -0.284 -0.078 -0.119 -0.161 -0.230 -0.315 -0.144

ses_int_log -0.181 -0.172 -0.205 -0.169 -0.253 -0.056 -0.202 -0.171 -0.134 -0.078 -0.051 -0.085 -0.103 0.023 0.002 -0.057 -0.071 -0.033 -0.067 -0.022 -0.298

cov_sess 1.201 3.346 5.755 7.596 8.216 1.469 3.611 4.420 6.525 6.780 1.468 2.270 3.072 3.811 4.831 0.952 2.031 3.008 4.225 5.122 2.287

hxdsh 0.945 0.699 0.444 0.631 0.561 0.718 0.879 0.984 0.977 0.931 0.340 0.340 0.374 0.357 0.548 0.305 0.261 0.259 0.432 0.458 0.535

hxtrauma 0.577 0.516 0.587 0.457 0.379 0.373 0.333 0.537 0.490 0.292 0.144 0.080 0.256 0.045 0.115 0.225 0.212 0.365 0.247 0.225 0.221

si_2 si_3 si_4 si_5 ac_1 age sex_mf ss_nt_ cv_sss hxdsh hxtram

pb_1

pb_2

pb_3

pb_4

pb_5

tb_1

tb_2

tb_3

tb_4

tb_5

bhs_1

bhs_2

bhs_3

bhs_4

bhs_5

dep_1

dep_2

dep_3

dep_4

dep_5

si_1

si_2 0.000

si_3 0.000 0.000

si_4 0.000 0.000 0.000

si_5 0.000 0.000 0.000 0.000

ac_1 8.672 5.266 5.929 8.280 41.951

age 1.293 1.204 1.426 -0.156 -1.896 8.973

sex_mf 0.065 0.282 -0.111 -0.215 0.078 0.283 0.206

ses_int_log -0.151 -0.164 -0.122 0.002 -0.022 -0.002 0.007 0.036

cov_sess 3.314 3.893 5.041 4.449 0.992 -0.736 -0.097 -0.085 4.649

hxdsh 0.341 0.104 0.329 0.162 0.377 0.103 -0.050 -0.001 -0.003 0.208

hxtrauma 0.536 0.365 0.559 0.197 0.192 0.142 -0.035 0.001 -0.045 0.072 0.246

>

Terrence Jorgensen

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Sep 17, 2021, 9:02:17 AM9/17/21

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You are correlating auxiliaries with residuals of variables that have 0 residual variance because they are treated as single-indicator factors to enter the model. I don't think you need to worry about this warning message, but if you want to investigate further (e.g., to see if it is really NPD, which still might be nothing to worry about), then you have to manually incorporate the auxiliaries into your syntax by correlating them with the single-indicator factors (which have variance) rather than the observed counterparts (whose variances are restricted to zero so that all variance is represented in the factor)

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

Atanas Janackovski

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Sep 17, 2021, 9:25:10 AM9/17/21

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Thanks so much Terence. Just to be sure, I would run this via the regular lavaan function and not the semTools wrapper?

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Atanas Janackovski

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Sep 17, 2021, 9:45:28 AM9/17/21

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I have added the below to the syntax to incorporate the auxiliary variables into the model, however not sure that I have done this correctly as I am getting the error. Any guidance on what I may be doing wrong would be greatly appreciated. Thanks again.

Error in solve.default(H, A) :
Lapack routine dgesv: system is exactly singular: U[1,1] = 0
In addition: Warning messages:
1: In lav_data_full(data = data, group = group, cluster = cluster, :
lavaan WARNING: some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate
2: In lavaan(riclpm_cov_mod, data = phd_fin_wide, missing = "ML", estimator = "MLR", :
lavaan WARNING:
Model estimation FAILED! Returning starting values.

wpb_1 + wpb_2 + wpb_3 + wpb_4 + wpb_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma

wtb_1 + wtb_2 + wtb_3 + wtb_4 + wtb_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma
wbhs_1 + wbhs_2 + wbhs_3 + wbhs_4 + wbhs_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma
wdep_1 + wdep_2 + wdep_3 + wdep_4 + wdep_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma
wsi_1 + wsi_2 + wsi_3 + wsi_4 + wsi_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma

Atanas Janackovski

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Sep 17, 2021, 4:20:41 PM9/17/21

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Should I also model the covariates as time invariant predictors of the factor scores like one would do on a linear regression model on addition to correlating them?

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/74c6396b-b3b3-48bd-bc3e-9a6621b527d9n%40googlegroups.com.

Atanas Janackovski

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Sep 17, 2021, 4:56:33 PM9/17/21

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Actually, I found this link that gives an example in a growth model which I think should help:

https://quantdev.ssri.psu.edu/sites/qdev/files/GMCh5_LinearGrowthTimeInvariantCovariates_nr_0.html

Atanas Janackovski

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Sep 17, 2021, 8:06:27 PM9/17/21

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Okay, so I ran the model with the covariates incorporated into the model syntax and I do get an error re: the covariance matrix of the latent variables is not positive definite. Is this something I should be worried about?

+ Warning messages:

1: In lav_data_full(data = data, group = group, cluster = cluster, :
lavaan WARNING: some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate

2: 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::lavInspect(riclpm_cov_fit, "cov.lv")
       RIpb     RItb     RIbhs    RIdep    RIsi     wpb_1    wpb_2    wpb_3    wpb_4    wpb_5    wtb_1    wtb_2
RIpb    377.105
RItb    259.188 355.364
RIbhs   217.274 133.198 170.321
RIdep   143.798 260.068   40.780 355.569
RIsi    138.832   46.889   45.759 138.965 350.969
wpb_1 -183.312 -139.161 -114.872 -88.681 -80.715   69.921
wpb_2 -170.349 -127.711 -106.680 -79.350 -75.612   38.420   49.657
wpb_3 -158.866 -119.073 -97.246 -70.926 -71.735   12.905   16.428   31.474
wpb_4 -146.326 -108.624 -91.606 -62.129 -60.275    1.713    2.294    1.610   18.646
wpb_5 -150.086 -111.661 -92.323 -64.221 -62.752    1.969    2.587    3.070    6.347   32.634
wtb_1 -123.008 -161.380 -63.973 -132.990 -23.451   39.977   25.637    9.436    1.385    1.466   53.341
wtb_2 -112.494 -150.125 -58.440 -125.746 -19.364   25.951   32.147   17.072    2.923    2.782   22.863   54.077
wtb_3 -101.032 -139.976 -50.493 -116.137 -16.621   11.284   14.841   19.525    4.779    3.491   10.142   22.877
wtb_4   -94.410 -133.733 -47.112 -112.784 -13.928    4.697    6.098    9.574   13.839    7.978    3.952    8.693
wtb_5   -96.292 -138.136 -48.593 -115.603 -10.685    4.529    5.953    7.274    6.851   14.526    3.357    6.269
wbhs_1 -108.009 -66.190 -83.345 -25.686 -27.197   24.692   20.122    6.465    0.986    1.084   17.439   13.870
wbhs_2 -98.278 -58.383 -77.120 -20.658 -23.168   12.757   18.701    6.846    1.234    1.304    8.665   16.386
wbhs_3 -95.272 -56.369 -74.539 -17.619 -21.146    7.859   10.437   10.445    2.783    2.498    5.802   11.097
wbhs_4 -93.755 -55.883 -74.237 -15.985 -18.734    5.383    7.094    8.103   10.402    6.312    3.950    7.263
wbhs_5 -90.743 -53.734 -72.882 -15.800 -16.723    3.024    3.987    4.475    5.207    8.723    2.167    3.854
wdep_1 -63.110 -131.283 -17.950 -179.698 -70.028   30.633   20.518    7.262    0.962    1.137   22.550   15.039
wdep_2 -54.017 -122.347 -13.156 -172.927 -65.876   20.119   24.521    9.775    1.145    1.503   13.465   19.558
wdep_3 -46.518 -116.373   -7.812 -167.279 -64.073    6.784    8.833   13.958    0.119    1.507    4.956    9.226
wdep_4 -41.124 -111.762   -5.659 -164.253 -58.689    3.294    4.311    5.355    7.453    4.266    2.208    3.632
wdep_5 -39.392 -111.547   -5.052 -164.867 -57.513    2.117    2.775    3.459    2.867   11.125    1.484    2.584
wsi_1   -53.663 -15.170 -17.474 -67.539 -162.634   23.385   19.452    7.324    0.779    1.086   13.327   10.338
wsi_2   -50.179 -15.543 -13.872 -65.433 -160.409    9.768   14.761   10.727    0.462    1.140    5.074    9.527
wsi_3   -52.740 -17.584 -13.681 -64.942 -161.977    5.285    6.497   19.199    1.020    1.628    4.449   10.670
wsi_4   -49.335 -12.419 -11.662 -63.469 -166.270    2.240    2.811    5.998    3.586    4.304    1.630    3.184
wsi_5   -53.354 -15.849 -15.357 -66.436 -168.333    1.515    1.925    3.858   -2.314    3.279    1.174    2.381
       wtb_3    wtb_4    wtb_5    wbhs_1   wbhs_2   wbhs_3   wbhs_4   wbhs_5   wdep_1   wdep_2   wdep_3   wdep_4
RIpb
RItb
RIbhs
RIdep
RIsi
wpb_1
wpb_2
wpb_3
wpb_4
wpb_5
wtb_1
wtb_2
wtb_3    50.267
wtb_4    15.917   39.272
wtb_5     7.980   15.158   38.374
wbhs_1    5.423    2.359    2.457   17.537
wbhs_2    5.130    2.563    2.887    8.594   13.415
wbhs_3   13.434    6.144    5.415    4.462    5.636   11.484
wbhs_4    8.793   14.952   12.211    2.960    3.521    6.500   15.459
wbhs_5    4.083    7.031   12.481    1.680    2.023    3.603    8.291   12.750
wdep_1    5.152    2.452    2.579   14.301    8.214    4.646    3.093    1.767   23.760
wdep_2    3.982    2.750    3.358   10.909   11.652    6.282    4.063    2.384   12.511   18.933
wdep_3   11.252    5.516    4.354    3.522    4.046    7.717    4.547    2.552    3.867    5.219   12.668
wdep_4    1.694   10.336    7.171    1.880    2.383    3.957    8.040    4.951    2.060    3.080    2.852   11.200
wdep_5    2.264    5.891   12.718    1.176    1.433    2.483    5.073    8.096    1.265    1.781    2.000    4.729
wsi_1     3.355    2.024    2.491   10.671    9.244    4.517    2.998    1.757   14.940   11.783    4.012    2.205
wsi_2     4.415    2.845    2.756    3.869    6.558    4.458    3.129    1.813    5.789   10.290    5.697    2.374
wsi_3    16.824   13.093    3.035    2.456    2.837    7.735    2.041    0.553    3.068    4.430   12.751    1.750
wsi_4     2.747    9.271    1.139    1.188    1.458    2.638    3.996    1.218    1.401    2.154    1.742    3.988
wsi_5     3.346    5.858    5.976    0.755    0.829    1.625    1.994    3.073    0.851    1.133    1.937    0.176
       wdep_5   wsi_1    wsi_2    wsi_3    wsi_4    wsi_5
RIpb
RItb
RIbhs
RIdep
RIsi
wpb_1
wpb_2
wpb_3
wpb_4
wpb_5
wtb_1
wtb_2
wtb_3
wtb_4
wtb_5
wbhs_1
wbhs_2
wbhs_3
wbhs_4
wbhs_5
wdep_1
wdep_2
wdep_3
wdep_4
wdep_5   13.325
wsi_1     1.301   64.819
wsi_2     1.433   13.404   37.737
wsi_3     1.133    2.988    6.394   44.646
wsi_4     1.542    1.442    2.062    8.404   41.526
wsi_5     2.891    0.819    1.276    4.721   14.670   32.516
>

Terrence Jorgensen

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Sep 18, 2021, 2:51:35 AM9/18/21

to lavaan

the covariance matrix of the latent variables is not positive definite. Is this something I should be worried about?

Not sure. I don't see any negative variances, but you requested the marginal covariance matrix, not residual.

lavInspect(riclpm_cov_fit, "est")$psi # actual estimates

You could check the correlation matrix for values > 1

any(lavInspect(riclpm_cov_fit, "cor.lv") > 1) # marginal

any(lavInspect(riclpm_cov_fit, "est")$psi > 1) # residual

If there are no specific Heywood cases, then it is a case of linear dependency in the residual covariance matrix, which can be hard to track down the source of. But if your determinant or smallest eigenvalue are nearly zero (only a little negative, way out in the decimal places), then I wouldn't worry about it.

Just to check you implemented the saturated correlates approach as described in the Enders citation (see References on the ?auxiliary help page), does this model have the same df as the model without any auxiliaries? To address an earlier question, the point is to not change the substantive interpretation of your model or its df, by allowing each auxiliary to correlate with each observed variable's residual (which you put in the latent space) and with other auxiliaries.

Atanas Janackovski

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Sep 18, 2021, 8:14:32 AM9/18/21

to lavaan

Sorry about that… This is all new to me, so I truly appreciate the patience and help. Okay, so I think I have updated the syntax as per the Enders' citation, because my above syntax was clearly wrong… I have included the syntax further below, and now I'm not getting any warnings apart from the below, which I hope I don't have to worry about.

lavaan WARNING: some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate

The added syntax is:

## ==========
## cov variances
## ==========
ac_1 ~~ ac_1
age ~~ age
sex_mf ~~ sex_mf
cov_sess ~~ cov_sess
hxdsh ~~ hxdsh
hxtrauma ~~ hxtrauma
ses_int_log ~~ ses_int_log
## ==========
## cov covariances
## ==========
ac_1 ~~ age + sex_mf + cov_sess + hxdsh + hxtrauma + ses_int_log
age ~~ sex_mf + cov_sess + hxdsh + hxtrauma + ses_int_log
sex_mf ~~ cov_sess + hxdsh + hxtrauma + ses_int_log
cov_sess ~~ hxdsh + hxtrauma + ses_int_log
hxdsh ~~ hxtrauma + ses_int_log
hxtrauma ~~ ses_int_log
## ==========
## cov covs
## ==========
wpb_1 + wpb_2 + wpb_3 + wpb_4 + wpb_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma # nolint
wtb_1 + wtb_2 + wtb_3 + wtb_4 + wtb_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma # nolint
wbhs_1 + wbhs_2 + wbhs_3 + wbhs_4 + wbhs_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma # nolint
wdep_1 + wdep_2 + wdep_3 + wdep_4 + wdep_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma # nolint
wsi_1 + wsi_2 + wsi_3 + wsi_4 + wsi_5 ~~ ac_1 + age + sex_mf + ses_int_log + cov_sess + hxdsh + hxtrauma # nolint

I'm getting very similar estimates to the semTools wrapper, and the model has the same dfs. I think I understand this now… The only questions I have is when bringing the aux vars into the model, should they be constrained so that they are the same for each variable over multiple time points? e.g.

wpb_1 + wpb_2 + wpb_3 + wpb_4 + wpb_5 ~~ s1*ac_1 + s2*age + s3*sex_mf + s4*ses_int_log + s5*cov_sess + hxdsh + hxtrauma # nolint

Thanks again,

Atanas

Terrence Jorgensen

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Oct 4, 2021, 3:47:48 AM10/4/21

to lavaan

The only questions I have is when bringing the aux vars into the model, should they be constrained so that they are the same for each variable over multiple time points? e.g.

With constraints, the correlates would no longer be saturated. I don't think it is necessary to do this, and is sort of at odds with the idea that these are auxiliary variables about which we have no hypotheses except that they can relate to missing values. Allowing their coefficients to vary over time is essentially moderation by time, which can't be ruled out.

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