R-sig-mixed-models Digest, Vol 136, Issue 41
Thank you for explaining this. This is *very* interesting. As far as I understand, m_zcp5 is the model Reinhold Kliegl uses in this RPub article[1] (actually m_zcp7 which should be identical). Also Barr et al. (2013)[2], Bates et al. (2015)[3] and Matuschek et al. (2017)[4] suggest similar models as the first step for model reduction. However, their categorical independent variables have only two levels and they work with crossed random effects. cake3 <- cake cake3 <- subset(cake3, recipe != "C") cake3$recipe <- factor(cake3$recipe) contrasts(cake3$recipe) <- c(0.5, -0.5) # Barr and Matuschek use effect coding m_zcp5 <- lmer_alt(angle ~ recipe + (recipe || replicate), cake3) VarCorr(m_zcp5) Groups Name Std.Dev. replicate (Intercept) 5.8077 replicate.1 re1.recipe1 1.8601 Residual 5.5366 cake3$recipe_numeric <- ifelse(cake3$recipe == "A", 0.5, -0.5) m_zcp7 <- lmer(angle ~ recipe_numeric + (1|replicate) + (0 + recipe_numeric|replicate), cake3) VarCorr(m_zcp7) Groups Name Std.Dev. replicate (Intercept) 5.8077 replicate.1 recipe_numeric 1.8601 Residual 5.5366 Besides that, Reinhold Kliegl reduces m_zcp5 to Model3b - i.e. (recipe || replicate) to (1 | replicate) + (1 | recipe:replicate). Whereas you, If I understand correctly, suggest reducing/comparing (0 + recipe || replicate) to (1 | recipe:replicate). Why is that? Am I missing something? Cheers, Maarten [1] https://rpubs.com/Reinhold/22193 [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3881361/ [3] https://arxiv.org/abs/1506.04967 vignettes here: https://github.com/dmbates/RePsychLing/tree/master/vignettes [4] https://arxiv.org/abs/1511.01864
On Wed, May 2, 2018 at 11:56 AM, Rune Haubo <rune.haubo at gmail.com> wrote:
On 2 May 2018 at 00:27, Maarten Jung <Maarten.Jung at mailbox.tu-dresden.de> wrote:
Sorry, I forgot that lmer() (unlike lmer_alt() from the afex package)
does not convert factors to numeric covariates when using the the
double-bar notation!
The model I was talking about would be:
m_zcp5 <- lmer_alt(angle ~ recipe + (recipe || replicate), cake)
VarCorr(m_zcp5)
Groups Name Std.Dev.
replicate (Intercept) 6.2359
replicate.1 re1.recipe1 1.7034
replicate.2 re1.recipe2 0.0000
Residual 5.3775
This model seems to differ (and I don't really understand why) from
m_zcp6 which I think is equivalent to your m_zcp4:
m_zcp6 <- lmer_alt(angle ~ recipe + (0 + recipe || replicate), cake)
VarCorr(m_zcp6)
Groups Name Std.Dev.
replicate re1.recipeA 5.0429
replicate.1 re1.recipeB 6.6476
replicate.2 re1.recipeC 7.1727
Residual 5.4181
anova(m_zcp6, m_zcp5, refit = FALSE)
Data: data
Models:
m_zcp6: angle ~ recipe + ((0 + re1.recipeA | replicate) + (0 + re1.recipeB |
m_zcp6: replicate) + (0 + re1.recipeC | replicate))
m_zcp5: angle ~ recipe + ((1 | replicate) + (0 + re1.recipe1 | replicate) +
m_zcp5: (0 + re1.recipe2 | replicate))
Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
m_zcp6 7 1781.8 1807.0 -883.88 1767.8
m_zcp5 7 1742.0 1767.2 -863.98 1728.0 39.807 0 < 2.2e-16 ***
Yes, m_zcp4 and m_zcp6 are identical. For m_zcp5 I get: m_zcp5 <- lmer_alt(angle ~ recipe + (recipe || replicate), cake) VarCorr(m_zcp5) Groups Name Std.Dev. replicate (Intercept) 6.0528e+00 replicate.1 re1.recipeB 5.8203e-07 replicate.2 re1.recipeC 2.1303e+00 Residual 5.4693e+00 and if we change the reference level for recipe we get yet another result: cake2 <- cake cake2$recipe <- relevel(cake2$recipe, "C") m_zcp5b <- lmer_alt(angle ~ recipe + (recipe || replicate), cake2) VarCorr(m_zcp5b) Groups Name Std.Dev. replicate (Intercept) 6.5495e+00 replicate.1 re1.recipeA 2.5561e+00 replicate.2 re1.recipeB 1.0259e-07 Residual 5.4061e+00 This instability indicates that something fishy is going on... The correlation parameters are needed in the "default" representation: (recipe | replicate) and (0 + recipe | replicate) are equivalent because the correlation parameters make the "appropriate adjustments", but (recipe || replicate) is _not_ the same as (0 + recipe || replicate) with afex::lmer_alt. I might take it as far as to say that (recipe | replicate) is meaningful because it is a re-parameterization of (0 + recipe | replicate). On the other hand, while the diagonal variance-covariance matrix parameterized by (0 + recipe || replicate) is meaningful, a model with (recipe || replicate) using afex::lmer_alt does _not_ make sense to me (and does not represent a diagonal variance-covariance matrix).
Do m_zcp5 and Model3b estimate the same random effects in this case?
Well, Model3b makes sense while m_zcp5 does not, but Model3b estimates
more random effects than the others:
Model3b <- lmerTest::lmer(angle ~ recipe + (1 | replicate) + (1 |
recipe:replicate),
data=cake)
length(unlist(ranef(Model3b))) # 60
length(unlist(ranef(m_zcp4))) # 45 - same for m_zcp, m_zcp2 and m_zcp6
and Model2
If not, what is the difference between m_zcp5 and Model3b (except for the fact that the variance depends on the recipe in m_zcp5) and which one is the more complex model?
There is no unique 'complexity' ordering, for example, Model3b use 2 random-effect variance-covariance parameters to represent 60 random effects, while m_zcp4 (m_zcp2) use 3 (6) random-effect variance-covariance parameters to represent 45 random effects. But usually the relevant 'complexity' scale is the number of parameters, cf. likelihood ratio tests, AIC, BIC etc. There are corner-cases, however; if x1 and x2 are continuous then (1 + x1 + x2 | group) and '(1 + x1 | group) + (1 + x2 | group)' both use 6 random-effect variance-covariance parameters, but the models represent different structures and you can argue that the latter formulation is less complex than the former since it avoids the correlation between x1 and x2. Cheers, Rune
I would be glad if you could elaborate on this and help me and the others understand these models. Cheers, Maarten