Rasch with lme4
Daniel Ezra Johnson wrote:
In the output for this model:
M2 = lm(Reaction ~ Days + Sex + factor(Subject), sleepstudy) summary(M2)
You will see that one of the coefficients is NA. If you put factor(Subject) before Sex it would be SexMale that comes out NA. Nested fixed effects will always return an error (or incomplete model), unless I'm completely mistaken.
Complete output pasted below. It's been a long day, but I cannae see an
NA! Is your output different?
My intuition tells me that order of the variables shouldn't affect these
estimates as addition is commutative. I imagine they would affect a
call to a (sequential) "anova" as this determines the order of nested
model comparisons from the order of the variables.
A
> M2a = lm(Reaction ~ Days + Sex + factor(Subject), sleepstudy)
> summary(M2a)
Call:
lm(formula = Reaction ~ Days + Sex + factor(Subject), data = sleepstudy)
Residuals:
Min 1Q Median 3Q Max
-101.4284 -17.2881 0.2311 15.2005 132.6242
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 293.6628 10.8062 27.176 < 2e-16 ***
Days 10.4511 0.8067 12.956 < 2e-16 ***
SexMale 2.4017 4.6864 0.512 0.609020
factor(Subject)309 -126.6607 13.8995 -9.113 3.18e-16 ***
factor(Subject)310 -111.1326 13.8915 -8.000 2.37e-13 ***
factor(Subject)330 -38.6722 13.8995 -2.782 0.006047 **
factor(Subject)331 -32.6978 13.8915 -2.354 0.019798 *
factor(Subject)332 -34.8318 13.8915 -2.507 0.013160 *
factor(Subject)333 -25.7353 13.8995 -1.852 0.065935 .
factor(Subject)334 -46.8318 13.8915 -3.371 0.000938 ***
factor(Subject)335 -91.8236 13.8995 -6.606 5.55e-10 ***
factor(Subject)337 33.5872 13.8915 2.418 0.016737 *
factor(Subject)349 -66.0592 13.8995 -4.753 4.44e-06 ***
factor(Subject)350 -28.5312 13.8915 -2.054 0.041618 *
factor(Subject)351 -51.7959 13.8995 -3.726 0.000269 ***
factor(Subject)352 -4.7123 13.8915 -0.339 0.734889
factor(Subject)369 -36.0992 13.8915 -2.599 0.010234 *
factor(Subject)370 -50.1919 13.8995 -3.611 0.000408 ***
factor(Subject)371 -47.1498 13.8915 -3.394 0.000868 ***
factor(Subject)372 -24.0075 13.8995 -1.727 0.086056 .
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 31.06 on 160 degrees of freedom
Multiple R-squared: 0.7282, Adjusted R-squared: 0.6959
F-statistic: 22.56 on 19 and 160 DF, p-value: < 2.2e-16
>
> M2b = lm(Reaction ~ Days + factor(Subject) + Sex, sleepstudy)
> summary(M2b)
Call:
lm(formula = Reaction ~ Days + factor(Subject) + Sex, data = sleepstudy)
Residuals:
Min 1Q Median 3Q Max
-101.4284 -17.2881 0.2311 15.2005 132.6242
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 293.6628 10.8062 27.176 < 2e-16 ***
Days 10.4511 0.8067 12.956 < 2e-16 ***
factor(Subject)309 -126.6607 13.8995 -9.113 3.18e-16 ***
factor(Subject)310 -111.1326 13.8915 -8.000 2.37e-13 ***
factor(Subject)330 -38.6722 13.8995 -2.782 0.006047 **
factor(Subject)331 -32.6978 13.8915 -2.354 0.019798 *
factor(Subject)332 -34.8318 13.8915 -2.507 0.013160 *
factor(Subject)333 -25.7353 13.8995 -1.852 0.065935 .
factor(Subject)334 -46.8318 13.8915 -3.371 0.000938 ***
factor(Subject)335 -91.8236 13.8995 -6.606 5.55e-10 ***
factor(Subject)337 33.5872 13.8915 2.418 0.016737 *
factor(Subject)349 -66.0592 13.8995 -4.753 4.44e-06 ***
factor(Subject)350 -28.5312 13.8915 -2.054 0.041618 *
factor(Subject)351 -51.7959 13.8995 -3.726 0.000269 ***
factor(Subject)352 -4.7123 13.8915 -0.339 0.734889
factor(Subject)369 -36.0992 13.8915 -2.599 0.010234 *
factor(Subject)370 -50.1919 13.8995 -3.611 0.000408 ***
factor(Subject)371 -47.1498 13.8915 -3.394 0.000868 ***
factor(Subject)372 -24.0075 13.8995 -1.727 0.086056 .
SexMale 2.4017 4.6864 0.512 0.609020
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 31.06 on 160 degrees of freedom
Multiple R-squared: 0.7282, Adjusted R-squared: 0.6959
F-statistic: 22.56 on 19 and 160 DF, p-value: < 2.2e-16