Lavaan warning

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Eliseo Fica

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Nov 23, 2021, 2:45:01 PM11/23/21

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Hi community,

I´m fitting a model and a I get the following warning message:

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.

This is the model:

MOD3 <- '

# Measurement model

illegality =~ lvl_insti + mkt_chain

macro =~ vulnera + inequa + pov_ratio + gdp_grth + grth_00_20

institution =~ crpt_agents + gov_ind + gdp_grth

perception =~ inj_perc + mtv_perp

# Regressions

illegality ~ macro

illegality ~ institution

illegality ~ perception

illegality ~ pov_perp + cult_root + nat_cap

pov_perp ~ macro

# Correlations

gov_ind ~~ vulnera

gov_ind ~~ inequa

gov_ind ~~ pov_ratio

gov_ind ~~ gdp_grth

gov_ind ~~ grth_00_20

vulnera ~~ gdp_grth

pov_ratio ~~ gdp_grth

inequa ~~ crpt_agents

lvl_insti ~~ inj_perc

vulnera ~~ pov_ratio

crpt_agents ~~ inj_perc

lvl_insti ~~ mtv_perp

macro ~~ nat_cap

The inspection

lvl_ns mkt_ch vulner inequa pov_rt gdp_gr g_00_2 crpt_g gov_nd inj_pr mtv_pr pv_prp clt_rt nat_cp

lvl_insti 0.337

mkt_chain 0.000 0.650

vulnera 0.000 0.000 0.427

inequa 0.000 0.000 0.000 0.322

pov_ratio 0.000 0.000 -0.186 0.000 0.592

gdp_grth 0.000 0.000 0.182 0.000 -0.373 0.842

grth_00_20 0.000 0.000 0.000 0.000 0.000 0.000 0.425

crpt_agents 0.000 0.000 0.000 -0.055 0.000 0.000 0.000 0.833

gov_ind 0.000 0.000 -0.494 -0.428 -0.252 -0.031 -0.297 0.000 0.755

inj_perc 0.264 0.000 0.000 0.000 0.000 0.000 0.000 -0.214 0.000 0.880

mtv_perp 0.251 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.707

pov_perp 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.964

cult_root 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000

nat_cap 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 1.000

And the outcome of the model:

lavaan 0.6-7 ended normally after 78 iterations

Estimator DWLS

Optimization method NLMINB

Number of free parameters 49

Number of observations 190

Model Test User Model:

Standard Robust

Test Statistic 54.654 71.532

Degrees of freedom 56 56

P-value (Chi-square) 0.526 0.079

Scaling correction factor 0.990

Shift parameter 16.350

simple second-order correction

Model Test Baseline Model:

Test statistic 966.383 565.569

Degrees of freedom 91 91

P-value 0.000 0.000

Scaling correction factor 1.845

User Model versus Baseline Model:

Comparative Fit Index (CFI) 1.000 0.967

Tucker-Lewis Index (TLI) 1.002 0.947

Robust Comparative Fit Index (CFI) NA

Robust Tucker-Lewis Index (TLI) NA

Root Mean Square Error of Approximation:

RMSEA 0.000 0.038

90 Percent confidence interval - lower 0.000 0.000

90 Percent confidence interval - upper 0.043 0.063

P-value RMSEA <= 0.05 0.981 0.763

Robust RMSEA NA

90 Percent confidence interval - lower 0.000

90 Percent confidence interval - upper NA

Standardized Root Mean Square Residual:

SRMR 0.052 0.052

Parameter Estimates:

Standard errors Robust.sem

Information Expected

Information saturated (h1) model Unstructured

Latent Variables:

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

illegality =~

lvl_insti 1.000

mkt_chain 0.727 0.132 5.486 0.000

macro =~

vulnera 1.000

inequa 1.088 0.101 10.781 0.000

pov_ratio 0.844 0.113 7.452 0.000

gdp_grth -0.026 0.162 -0.158 0.874

grth_00_20 1.002 0.110 9.145 0.000

institution =~

crpt_agents 1.000

gov_ind 1.212 0.357 3.397 0.001

gdp_grth -0.995 0.367 -2.713 0.007

perception =~

inj_perc 1.000

mtv_perp 1.563 0.813 1.923 0.054

Regressions:

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

illegality ~

macro -0.365 0.183 -1.999 0.046

institution -1.315 0.746 -1.764 0.078

perception -1.036 1.055 -0.982 0.326

pov_perp 0.178 0.062 2.877 0.004

cult_root 0.287 0.075 3.811 0.000

nat_cap 0.177 0.082 2.158 0.031

pov_perp ~

macro -0.250 0.099 -2.517 0.012

Covariances:

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

.vulnera ~~

.gov_ind -0.494 0.092 -5.377 0.000

.inequa ~~

.gov_ind -0.428 0.101 -4.253 0.000

.pov_ratio ~~

.gov_ind -0.252 0.092 -2.743 0.006

.gdp_grth ~~

.gov_ind -0.031 0.079 -0.398 0.690

.grth_00_20 ~~

.gov_ind -0.297 0.095 -3.120 0.002

.vulnera ~~

.gdp_grth 0.182 0.051 3.565 0.000

.pov_ratio ~~

.gdp_grth -0.373 0.054 -6.955 0.000

.inequa ~~

.crpt_agents -0.055 0.048 -1.145 0.252

.lvl_insti ~~

.inj_perc 0.264 0.082 3.219 0.001

.vulnera ~~

.pov_ratio -0.186 0.058 -3.205 0.001

.crpt_agents ~~

.inj_perc -0.214 0.070 -3.080 0.002

.lvl_insti ~~

.mtv_perp 0.251 0.091 2.748 0.006

macro ~~

nat_cap 0.169 0.056 3.009 0.003

institution -0.151 0.051 -2.939 0.003

perception -0.091 0.051 -1.788 0.074

institution ~~

perception 0.083 0.046 1.807 0.071

Variances:

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

.lvl_insti 0.337 0.146 2.308 0.021

.mkt_chain 0.650 0.088 7.359 0.000

.vulnera 0.427 0.081 5.252 0.000

.inequa 0.322 0.064 5.040 0.000

.pov_ratio 0.592 0.060 9.811 0.000

.gdp_grth 0.842 0.148 5.696 0.000

.grth_00_20 0.425 0.078 5.414 0.000

.crpt_agents 0.833 0.096 8.697 0.000

.gov_ind 0.755 0.115 6.562 0.000

.inj_perc 0.880 0.098 8.964 0.000

.mtv_perp 0.707 0.218 3.237 0.001

.pov_perp 0.964 0.114 8.428 0.000

nat_cap 1.000 0.089 11.200 0.000

.illegality 0.044 0.175 0.249 0.803

macro 0.573 0.093 6.149 0.000

institution 0.167 0.065 2.580 0.010

perception 0.120 0.078 1.538 0.124

cult_root 1.000 0.043 23.499 0.000

What do you think that is the problem here? I hope you can help me.

Thanks a lot.

Edward Rigdon

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Nov 23, 2021, 3:46:41 PM11/23/21

to lav...@googlegroups.com

The warning is probably triggered by gov_ind. You can see in the lavInspect output that gov_ind has residual covariances with vulner and inequa that are higher than the residual variances of vulner and inequa, implying residual correlations outside the expected (-1, +1) range. I don't know why that is, but this seems like a strong rejection of the current model structure.

You have gdp_grth loading on two factors, macro and institution, and the first loading is near 0. Your results might change if you delete the near-0 loading.

--Ed Rigdon

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