[R-sig-ME] Order of terms for random slopes

[Stefan Th. Gries]

Hi all

I have a question about how the ordering of variable names in the
random effects structure of an lmer model leads to different results.
These are the data:

###############
x <- structure(list(OVERLAParcsine = c(0.232077682862713, 0.656060590924923,
0.546850950695944, 0.668742703202372, 0.631058840778021, 0.433445320069886,
0.315193032440724, 0.656060590924923, 0.389796296474261, 0.455598673395823,
0.500654712404588, 0.477995198518952, 0.304692654015398, 0.631058840778021,
0.489290778014116, 0.694498265626556, 0.656060590924923, 0.466765339047296,
0.411516846067488, 0.582364237868743, 0.33630357515398, 0.36826789343664,
0.489290778014116, 0.582364237868743, 0.283794109208328, 0.631058840778021,
0.33630357515398, 0.606505855213087, 0.512089752934148, 0.150568272776686,
0.273393031467473, 0.466765339047296, 0.160690652951911, 0.120289882394788,
0.558600565342801, 0.400631592701372, 0.273393031467473, 0.72081876087009,
0.444492776935819, 0.681553211563117, 0.546850950695944, 0.523598775598299,
0.273393031467473, 0.694498265626556, 0.294226837748982, 0.500654712404588,
0.411516846067488, 0.618728690672251), NAME = structure(c(1L,
2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 1L, 2L, 3L, 4L,
5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 1L, 2L, 3L, 4L, 5L, 6L, 7L,
8L, 9L, 10L, 11L, 12L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
11L, 12L), .Label = c("Anne", "Aran", "Becky", "Carl", "Dominic",
"Gail", "Joel", "John", "Liz", "Nicole", "Ruth", "Warren"), class = "factor"),
    PERSON = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("caretaker",
    "child"), class = "factor"), PHASE = c(1L, 1L, 1L, 1L, 1L,
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
    2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
    1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L)), class =
"data.frame", row.names = c(NA, -48L))
###############

With the following order of variables in the random-effects structure,
I get convergence warnings,

###############
summary(m1a <- lme4::lmer(OVERLAParcsine ~ 1+PERSON*PHASE +
(1+PERSON+PHASE|NAME), data=x), correlation=F) # warning
   logLik(m1a) # 31.89056
###############

but not with this order:

###############
summary(m1b <- lme4::lmer(OVERLAParcsine ~ 1+PERSON*PHASE +
(1+PHASE+PERSON|NAME), data=x), correlation=F) # fine
   logLik(m1b) # 31.89128
###############

Why does the order of the random effects matter when PHASE is still
considered numeric? Thanks for any input you may have,
STG