Conflicting p-values from pvals.fnc

Simpler model with random slopes

Hi all,

this question is ultimately based on Florian's lecture1 slides here:
http://hlplab.wordpress.com/2010/05/10/mini-womm/

I'm doing a mixed model logistic regression, with random intercepts
for items and random slopes for items with respect to the fixed effect
Indep2 (cf. slide 85):

(a) glmer(formula = Dep ~ 1 + (1 | Item) + (0 + Indep2 | Item) +
Indep1 + Indep2, data = my.data, family = binomial(link = "logit"))

As per slide 88, I can also reduce the random effects to (1 + Indep2 | Item):

(b) glmer(formula = Dep ~ 1 + (1 + Indep2 | Item) + Indep1 + Indep2,
data = my.data, family = binomial(link = "logit"))

It's not exactly clear to me what (1 + Indep2 | Item) does, since the
output of both (a) and (b) includes random intercepts for items and
random slopes for items by Indep2. At the same time, model (a) and (b)
differ in their exact estimates.

I would appreciate if someone could explain what the difference
between model (a) and (b) is.

Thanks
Sverre

Questions about reporting mixed-effects results

Dear all,

I have a few questions about how to report the results of mixed-effects analyses for publication. I have
been perusing the Jaeger & Kuperman presentation but a few questions remain.  

I have been asked by the reviewers to include a full regression table, which I take to comprise coefficient
estimates, MCMC-based confidence intervals and MCMC-based p-value estimations.
-Should the model that I use to report these values contain uncentered predictors, centered predictors,
or centered and scaled predictors?
-A few of my models involve random intercepts, and I believe that pvals.fnc() is not currently defined for
models with random intercepts.  Do you have any suggestions for how I should report these models? 

My models contain many control variables and only one or two variables that I am actually concerned with.  As
such, I have not worried about multicollinearity among the control variables.  I suppose I should just
state this somewhere to facilitate the interpretation of the regression tables?

Lastly, is there any way to do a power analysis for mixed-effects models?  One reviewer asked whether this
was possible and noted that there may be rough approximations such as "the t-approximation to the
coefficient-wise test".

Thank you!
Ariel

negative deviances (again)

questions about logit mixed model with R

Bielefeld Mixed Models Workshop 2012

Re: Collinearity and centering multi-level (more than 2 levels) fixed predictors

Hi,

I think part of my concern is Type 1 and Type 2 Errors. From my
experience with my own data, Type II error is a big concern, as I've
encountered cases where reducing collinearity changes test results
from non-significant to highly significant.

A tutorial that Dr. Jaeger created on mixed effects model does mention
that Type 1 error does not increase much in the presence of
collinearity. But if I recall correctly, there is an example in the
tutorial using the lexdec dataset where the presence of extremely high
collinearity causes an (?)overestimate of significance.

So in essence, without being able to reduce collinearity, I am afraid
of not being able to detect significances when there are in fact
significant differences (or vice versa), and interpreting coefficient
estimates is also problematic.

Thanks.

Best,
Xiao

Collinearity and centering multi-level (more than 2 levels) fixed predictors

Dear r-lang users,

I have a set of binary data from a 2 by 3 design study. I centered the
two-level predictor ('LHcenter': local & LD) but did not centered the
3 level predictor ('cond': A, B, & C). As you can see below in the
triangular matrix towards the end of the lmer output, there is
significant collinearity; the absolute values of some of the
correlations are above 0.6.

---8<----------------------------------------------------------------------------------------------------------------------------
>glmer(true ~ cond * LHcenter + (1 | subject) + (1 | items), data=offlineTarget, family=binomial)

Generalized linear mixed model fit by the Laplace approximation
Formula: true ~ cond * LHcenter + (1 | subject) + (1 | items)
   Data: offlineTarget
   AIC   BIC   logLik deviance
  747.8 785.9 -365.9    731.8

Random effects:
 Groups        Name    Variance     Std.Dev.
 items     (Intercept)     0.13838     0.37199
 subject   (Intercept)    1.44652     1.20271
Number of obs: 864, groups: items, 30; subject, 29

Fixed effects:
                          Estimate    Std. Error     z value      Pr(>|z|)
(Intercept)           -0.09775      0.30932      -0.316      0.75199
condB                  0.62445      0.25534       2.446      0.01446   *
condC                  0.70552      0.27286       2.586      0.00972   **
LHcenter              4.86821      0.42482      11.459      < 2e-16   ***
condB:LHcenter   -2.31392      0.51162      -4.523      6.1e-06    ***
condC:LHcenter   -1.00381      0.54643      -1.837       0.06621   .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
                       (Intr)    condB    condC    LHcntr    cnB:LH
condB            -0.526
condC            -0.491    0.607
LHcenter        -0.085    0.130      0.118
cndB:LHcntr    0.070   -0.053     -0.093      -0.801
cndC:LHcntr    0.066   -0.093      0.033      -0.735     0.607
---8<----------------------------------------------------------------------------------------------------------------------------

I also tested whether the interaction is significant by comparing the
full model with one without the interaction term:

glmer(true ~ cond * LHcenter + (1 | subject) + (1 | items),
data=offlineTarget, family=binomial)
glmer(true ~ cond  +  LHcenter + (1 | subject) + (1 | items),
data=offlineTarget, family=binomial)

And I observed a significant difference, suggesting that there is
significant interaction.

So I proceeded to conduct planned comparisons. To do so, I created a
new predictor in the table object by merging the two factors (a 3
level factor and a 2 level factor) together, resulting in a new factor
named 'posthoc_cond' with 6 levels: Local_A, Local_B, Local_C, LD_A,
LD_B, & LD_C

I conducted glmer WITHOUT centering the 6-level fixed predictor 'posthoc_cond'.

posthoc_result = glmer(true~posthoc_cond + (1|subject) + (1|item),
data=offlineTarget, family="binomial")

and then use glht() from 'multcomp' to conduct paired comparisons.

The problem with posthoc_result, again, is high collinearity (see below)
---8<----------------------------------------------------------------------------------------------------------------------------
Correlation of Fixed Effects:
                         (Intr)   pst_A_   p_B_LD   pst_B_   p_C_LD
psthc_cndA_    -0.865
psthc_cB_LD    -0.835  0.712
psthc_cndB_    -0.944  0.896         0.734
psthc_cC_LD    -0.928  0.810        0.779      0.896
psthc_cndC_     -0.891  0.925        0.710      0.914      0.834
---8<----------------------------------------------------------------------------------------------------------------------------

So my question is, in my case, what can be done to reduce
collinearity. It seems that centering those multi-level predictors is
not applicable in my case since I am interested in whether different
levels of the fixed predictors have different means. Centering these
multilevel predictors would not allow me to test that.

Thank you in advance for your help!!

Best,
Xiao

Re: ling-r-lang-L Digest, Vol 2, Issue 49

Figuring out maximum random effects in mixed-effect regression models

Helmert (or really any) contrasts, log-likelihood, and specificity