[R-sig-ME] Removing random intercepts before random slopes
Maarten Jung
M@@rten@Jung @ending from m@ilbox@tu-dre@den@de
Sat Sep 1 15:49:58 CEST 2018
> thanks for your answer, makes sense to me. I think removing the random intercepts should mostly increase the residual error and thus even
> increase the SEs for the fixed effects. Is this correct?
Fwiw: this quick test with the Machines data seems to support my speculation:
data("Machines", package = "MEMSS")
d <- Machines
xtabs(~ Worker + Machine, d) # balanced
mm <- model.matrix(~ 1 + Machine, d)
c1 <- mm[, 2]
c2 <- mm[, 3]
summary(lmerTest::lmer(score ~ 1 + c1 + c2 + (1 + c1 + c2 | Worker), d))
# Fixed effects:
# Estimate Std. Error df t value Pr(>|t|)
# (Intercept) 52.356 1.681 5.000 31.151 6.4e-07 ***
# c1 7.967 2.421 5.000 3.291 0.021693 *
# c2 13.917 1.540 5.000 9.036 0.000277 ***
summary(lmerTest::lmer(score ~ 1 + c1 + c2 + (0 + c1 + c2 | Worker), d))
### SEs increased:
# Fixed effects:
# Estimate Std. Error df t value Pr(>|t|)
# (Intercept) 52.3556 0.6242 41.0000 83.880 < 2e-16 ***
# c1 7.9667 3.5833 5.3172 2.223 0.073612 .
# c2 13.9167 1.9111 6.2545 7.282 0.000282 ***
summary(lmerTest::lmer(score ~ 1 + c1 + c2 + (1 + c1 + c2 || Worker), d))
# Fixed effects:
# Estimate Std. Error df t value Pr(>|t|)
# (Intercept) 52.356 1.679 5.004 31.188 6.31e-07 ***
# c1 7.967 2.426 5.002 3.284 0.021833 *
# c2 13.917 1.523 5.004 9.137 0.000262 ***
summary(lmerTest::lmer(score ~ 1 + c1 + c2 + (0 + c1 + c2 || Worker), d))
### SEs increased:
# Fixed effects:
# Estimate Std. Error df t value Pr(>|t|)
# (Intercept) 52.3556 0.6242 41.0000 83.880 < 2e-16 ***
# c1 7.9667 3.5833 5.3172 2.223 0.073612 .
# c2 13.9167 1.9111 6.2545 7.282 0.000282 ***
Still, I would be glad to hear any thoughts on this question:
> Why exactely would it be conceptually strange to have random slopes but not random intercepts?
> Because intercepts often represent some kind of baseline and, say subjects, will probably have different baselines (and thus a corresponding variance component estimated as > 0) if their slopes (i.e. effects) vary, or is there any other statistical reason why most people remove the random slopes first?
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