Warning message when estimating growth curve model using multiple imputation

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ginette lafit

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Nov 25, 2021, 10:32:11 AM11/25/21

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Hi! I've estimated a growth curve model using imputed data sets

alliance.model5 <- '

# intercept

i =~ 1*Time1 + 1*Time2 + 1*Time3 + 1*Time4 + 1*Time5

# slope

s =~ 0*Time1 + 1*Time2 + 2*Time3 + 3*Time4 + 4*Time5

# regressions

i ~ PANSSTOT

s ~ PANSSTOT

alliance.fit <- growth.mi(alliance.model5, imps, m=50, miPackage = "Amelia", seed = 12345, estimator = "MLM", group = "Group")

The summary seems ok:

> summary(alliance.fit, fit.measures=TRUE)

lavaan.mi object based on 50 imputed data sets.

See class?lavaan.mi help page for available methods.

Convergence information:

The model converged on 50 imputed data sets

Heywood cases detected for data set(s) 2, 5, 6, 7, 9, 11, 16, 17, 23, 24, 25, 34, 35, 39, 43, 48, 50

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 50 imputed data sets, and to calculate degrees of freedom for each parameter's t test and CI.

Robust corrections are made by pooling the naive chi-squared statistic across 50 imputations for which the model converged, then applying the average (across imputations) scaling factor to that pooled value.

To instead pool the robust test statistics, set test = "D2" and pool.robust = TRUE.

Model Test User Model:

Test statistic 16.848 17.570

Degrees of freedom 26 26

P-value 0.914 0.891

Scaling correction factor 0.959

Model Test Baseline Model:

Test statistic 119.224 93.054

Degrees of freedom 30 30

P-value 0.000 0.000

Scaling correction factor 1.281

User Model versus Baseline Model:

Comparative Fit Index (CFI) 1.000 1.000

Tucker-Lewis Index (TLI) 1.118 1.154

Robust Comparative Fit Index (CFI) 1.000

Robust Tucker-Lewis Index (TLI) 1.000

Root Mean Square Error of Approximation:

RMSEA 0.000 0.000

90 Percent confidence interval - lower 0.000 0.000

90 Percent confidence interval - upper 0.043 0.000

P-value RMSEA <= 0.05 0.960 0.943

Robust RMSEA 0.000

90 Percent confidence interval - lower 0.000

90 Percent confidence interval - upper 0.051

Standardized Root Mean Square Residual:

SRMR 0.082 0.082

Parameter Estimates:

Standard errors Robust.sem

Information Expected

Information saturated (h1) model Structured

Group 1 [1]:

Latent Variables:

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

i =~

Time1 1.000

Time2 1.000

Time3 1.000

Time4 1.000

Time5 1.000

s =~

Time1 0.000

Time2 1.000

Time3 2.000

Time4 3.000

Time5 4.000

Regressions:

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

i ~

PANSSTOT -0.092 0.288 -0.320 1209.867 0.749

s ~

PANSSTOT -0.046 0.078 -0.593 153.363 0.554

Covariances:

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

.i ~~

.s -6.782 21.795 -0.311 169.144 0.756

Intercepts:

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

.Time1 0.000

.Time2 0.000

.Time3 0.000

.Time4 0.000

.Time5 0.000

.i 60.040 19.247 3.119 1639.168 0.002

.s 3.348 4.997 0.670 197.872 0.504

Variances:

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

.Time1 181.372 129.880 1.396 2408.097 0.163

.Time2 65.523 38.462 1.704 174.463 0.090

.Time3 65.364 34.601 1.889 106.684 0.062

.Time4 35.129 26.188 1.341 112.181 0.182

.Time5 112.551 89.014 1.264 74.115 0.210

.i 223.827 106.528 2.101 291.731 0.036

.s 5.426 7.191 0.755 104.035 0.452

Group 2 [0]:

Latent Variables:

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

i =~

Time1 1.000

Time2 1.000

Time3 1.000

Time4 1.000

Time5 1.000

s =~

Time1 0.000

Time2 1.000

Time3 2.000

Time4 3.000

Time5 4.000

Regressions:

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

i ~

PANSSTOT -0.026 0.288 -0.089 5045.915 0.929

s ~

PANSSTOT -0.012 0.067 -0.176 548.388 0.861

Covariances:

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

.i ~~

.s -10.679 13.770 -0.776 114.111 0.440

Intercepts:

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

.Time1 0.000

.Time2 0.000

.Time3 0.000

.Time4 0.000

.Time5 0.000

.i 59.561 18.518 3.216 5680.245 0.001

.s 0.855 4.328 0.197 584.850 0.844

Variances:

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

.Time1 78.052 35.631 2.191 131.264 0.030

.Time2 56.301 19.420 2.899 145.010 0.004

.Time3 44.944 17.541 2.562 79.544 0.012

.Time4 45.634 18.701 2.440 70.070 0.017

.Time5 108.994 55.258 1.972 69.025 0.053

.i 209.235 68.717 3.045 459.628 0.002

.s 6.530 4.712 1.386 69.411 0.170

However, I got some warning messages:

Warning messages:

1: In lav_object_post_check(object) :

lavaan WARNING: some estimated lv variances are negative

2: In sqrt(var.lhs.value * var.rhs.value) : NaNs produced

3: In lav_start_check_cov(lavpartable = lavpartable, start = START) :

lavaan WARNING: starting values imply NaN for a correlation value;

variables involved are: i s [in block 1]

I'm afraid I don't know how to interpret these warnings. Does anyone have an idea of what might be going on?

Many thanks in advance!

Ginette

Terrence Jorgensen

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Nov 26, 2021, 8:28:34 AM11/26/21

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Warning messages:
1: In lav_object_post_check(object) :
lavaan WARNING: some estimated lv variances are negative
2: In sqrt(var.lhs.value * var.rhs.value) : NaNs produced
3: In lav_start_check_cov(lavpartable = lavpartable, start = START) :
lavaan WARNING: starting values imply NaN for a correlation value;
variables involved are: i s [in block 1]

I'm afraid I don't know how to interpret these warnings

2 and 3 follow from the first: you can't calculate a standardized parameter using a negative variance estimate (which is what the first warning is). As the messages above state, they can occur due to sampling error and might not be a problem. Your pooled estimated variances are all > 0.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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