Random Intercept

Membuat model intersep acak

m1 <- lmer(MATH ~ 1 + ESCS + (1 | CNTSCHID), data = pisa)

The result

summary(m1)

Linear mixed model fit by REML ['lmerMod']
Formula: MATH ~ 1 + ESCS + (1 | CNTSCHID)
   Data: pisa

REML criterion at convergence: 13670.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0591 -0.6366 -0.0336  0.6187  4.5086 

Random effects:
 Groups   Name        Variance Std.Dev.
 CNTSCHID (Intercept) 2184     46.73   
 Residual             2004     44.77   
Number of obs: 1297, groups:  CNTSCHID, 41

Fixed effects:
            Estimate Std. Error t value
(Intercept)  370.330      7.833  47.280
ESCS           4.326      1.474   2.934

Correlation of Fixed Effects:
     (Intr)
ESCS 0.290

ICC result

tab_model(m1)

	MATH
Predictors	Estimates	CI	p
(Intercept)	370.33	354.96 – 385.70	<0.001
ESCS	4.33	1.43 – 7.22	0.003
Random Effects
σ²	2004.21
τ₀₀ _CNTSCHID	2183.92
ICC	0.52
N _CNTSCHID	41
Observations	1297
Marginal R² / Conditional R²	0.005 / 0.524

Prediction plot

pisa$m1 <- predict(m1)

pisa %>% 
  ggplot(aes(ESCS, m1, color = CNTSCHID, group = CNTSCHID)) + 
  geom_smooth(se = F, method = lm) +
  theme_bw() +
  labs(x = "ESCS", 
       y = "Matematika", 
       color = "CNTSCHID")

QQ-plot

qqmath(ranef(m1, condVar = TRUE))

$CNTSCHID