Modelling interaction effect and interpretation
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Jürgen Schmidt
Oct 11, 2021, 7:42:58 AM10/11/21
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Dear Members,
I did in lavaan a pathanalysis (without latent variables) with 3 equations, 2 endogenous variables ("Unsicherheit" and "AFDID") were categorical. In a first step in the first model without an interaction effect in the first equation ("Unsicherheit" is the endogenous categorical variable). The modell-fit was acceptable (see the printout) and the main effects were all significant. In a second step in a second model it did the same with the exception of an interaction term between the variable "West_Ost" and the variable "essround_re" called "interaction2" in the first equation (I built one interaction-term).
The printout showed then an significant interaction effect, but the two main effects, involved in interaction-term-building, were not longer significant although they were significant in the first step without the interaction-term. Is this possible? Or is there any kind of computing error concerning my conception of the intercation effect. Have in mind: My interaction effect is built as a variable (0/1), which I created on the base of two other dummy-variables (variable "West-Ost" (0/1) and Variable "essround_re" (0/1)); I multiplied these two variables and the product was my interaction-variable "interaction2" (0/1-variable)??? Can anybody help me? Thank you very much.
Printout of the first model:
lavaan 0.6-9 ended normally after 65 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 17
Used Total
Number of observations 2810 5260
Model Test User Model:
Standard Robust
Test Statistic 16.323 17.900
Degrees of freedom 2 2
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.914
Shift parameter 0.038
simple second-order correction
Model Test Baseline Model:
Test statistic 532.816 512.787
Degrees of freedom 3 3
P-value 0.000 0.000
Scaling correction factor 1.039
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.973 0.969
Tucker-Lewis Index (TLI) 0.959 0.953
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Root Mean Square Error of Approximation:
RMSEA 0.050 0.053
90 Percent confidence interval - lower 0.030 0.032
90 Percent confidence interval - upper 0.074 0.077
P-value RMSEA <= 0.05 0.435 0.361
Robust RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA
Standardized Root Mean Square Residual:
SRMR 0.042 0.042
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Unsicherheit ~
essround_re 0.212 0.056 3.782 0.000 0.212 0.097
agea 0.006 0.001 4.246 0.000 0.006 0.102
West_Ost 0.247 0.059 4.172 0.000 0.247 0.106
Geschlecht 0.757 0.058 13.139 0.000 0.757 0.347
.....
Printout of the second modell:
lavaan 0.6-9 ended normally after 76 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 18
Used Total
Number of observations 2810 5260
Model Test User Model:
Standard Robust
Test Statistic 6.514 6.643
Degrees of freedom 4 4
P-value (Chi-square) 0.164 0.156
Scaling correction factor 1.100
Shift parameter 0.719
simple second-order correction
Model Test Baseline Model:
Test statistic 530.213 509.722
Degrees of freedom 3 3
P-value 0.000 0.000
Scaling correction factor 1.040
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.995 0.995
Tucker-Lewis Index (TLI) 0.996 0.996
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Root Mean Square Error of Approximation:
RMSEA 0.015 0.015
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.035 0.035
P-value RMSEA <= 0.05 0.999 0.999
Robust RMSEA NA
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper NA
Standardized Root Mean Square Residual:
SRMR 0.037 0.037
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Unsicherheit ~
essround_re 0.112 0.070 1.612 0.107 0.112 0.052
agea 0.006 0.001 4.149 0.000 0.006 0.100
West_Ost 0.135 0.084 1.611 0.107 0.135 0.058
Geschlecht 0.759 0.058 13.171 0.000 0.759 0.348
interaction2 0.256 0.118 2.176 0.030 0.256 0.085
Edward Rigdon
Oct 11, 2021, 9:01:11 PM10/11/21
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Jurgen--
Broadly, taking "statistically significance" to mark estimates as qualitatively different from each other is not consistent with guidance from the American Statistical Association (Wasserstein, Schirm & Lazar 2019):
. P-values change, but estimates don't go to zero. If you are not centering your main effects before creating interactions, you might try that, as it will make parameter estimates easier to interpret in light of the likely collinearity between main effects and interaction terms.
But to answer your question, this is not uncommon. If the interaction model is correct, then the model with main effects only is misspecified, and the predictors included in that model are correlated with the excluded interaction term. On the other hand, including the interaction term introduces another parameter to estimate plus collinearity, both of which make the solution less stable, and this can be reflected in larger standard errors. This appears to be happening in your results.
From another perspective, the model with interaction provides a better fit in the chi-square sense, so perhaps its estimates are more to be trusted?
--Ed Rigdon
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Terrence Jorgensen
Oct 13, 2021, 5:09:22 AM10/13/21
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The printout showed then an significant interaction effect, but the two main effects, involved in interaction-term-building, were not longer significant
Those aren't main effects anymore. They are simple effects (specifically, the effect of a focal predictor when a moderator == 0).
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
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