In this model you are doing a cross level interaction between teachers years of experience and gender differences. However, we are also looking at the random gender differences between schools.
m4_lme <- lme(popular ~ sex*texp, data = popula, random = ~ sex|school, method = "ML")
summary(m4_lme)Linear mixed-effects model fit by maximum likelihood
Data: popula
AIC BIC logLik
4261.85 4306.657 -2122.925
Random effects:
Formula: ~sex | school
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 0.6347377 (Intr)
sex 0.4692521 0.08
Residual 0.6264320
Fixed effects: popular ~ sex * texp
Value Std.Error DF t-value p-value
(Intercept) 3.313651 0.15954654 1898 20.769180 0e+00
sex 1.329479 0.13183479 1898 10.084432 0e+00
texp 0.110229 0.01013882 98 10.872007 0e+00
sex:texp -0.034025 0.00837995 1898 -4.060303 1e-04
Correlation:
(Intr) sex texp
sex -0.046
texp -0.909 0.042
sex:texp 0.042 -0.908 -0.046
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.93387434 -0.64733763 0.02294381 0.53272602 3.49150352
Number of Observations: 2000
Number of Groups: 100 Refit The Model In this model we are measuring the same thing as Model 1 however in this model we have changed the variable teachers years of experience to center to around zero. This model centers the covariates so basically centers the constant from every value of the variable and in this model that variable happens to be teachers experience.
m4a_lme <- lme(popular ~ sex*ctexp,
data = popula, random = ~ sex|school, method = "ML")
summary(m4a_lme)Linear mixed-effects model fit by maximum likelihood
Data: popula
AIC BIC logLik
4261.85 4306.657 -2122.925
Random effects:
Formula: ~sex | school
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 0.6347377 (Intr)
sex 0.4692521 0.08
Residual 0.6264320
Fixed effects: popular ~ sex * ctexp
Value Std.Error DF t-value p-value
(Intercept) 4.885851 0.06660875 1898 73.35149 0e+00
sex 0.844178 0.05510824 1898 15.31855 0e+00
ctexp 0.110229 0.01013882 98 10.87201 0e+00
sex:ctexp -0.034025 0.00837995 1898 -4.06030 1e-04
Correlation:
(Intr) sex ctexp
sex -0.044
ctexp -0.006 0.000
sex:ctexp 0.000 -0.004 -0.046
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.93387434 -0.64733763 0.02294381 0.53272602 3.49150352
Number of Observations: 2000
Number of Groups: 100 The two models below tell the same story and both have the same exact AIC & BIC scores, this tells us that neither model is a better fit than the other. In the second model when using Ctexp, centers this distribution making the mean around 0. What causes the different numerical values is actually the result of centering the covariate previously done in the analysis in order to control the outliers. This is done to see the effect on gender when teacher experience is set at zero.
htmlreg(list(m4_lme, m4a_lme))| Model 1 | Model 2 | ||
|---|---|---|---|
| (Intercept) | 3.31*** | 4.89*** | |
| (0.16) | (0.07) | ||
| sex | 1.33*** | 0.84*** | |
| (0.13) | (0.06) | ||
| texp | 0.11*** | ||
| (0.01) | |||
| sex:texp | -0.03*** | ||
| (0.01) | |||
| ctexp | 0.11*** | ||
| (0.01) | |||
| sex:ctexp | -0.03*** | ||
| (0.01) | |||
| AIC | 4261.85 | 4261.85 | |
| BIC | 4306.66 | 4306.66 | |
| Log Likelihood | -2122.92 | -2122.92 | |
| Num. obs. | 2000 | 2000 | |
| Num. groups | 100 | 100 | |
| p < 0.001, p < 0.01, p < 0.05 | |||