[R-sig-ME] Advice on Mixed Models
Ben Bolker
bbolker at gmail.com
Sat Mar 11 00:59:52 CET 2017
On 17-03-08 02:01 PM, Rose Rosei wrote:
> Dear Advisors
>
> Would you please advise me. I would like to fit my model, but I struggled
> to do it
>
>
> A= Applicant = 10 persons
> S= Stream ( four levels, 1, 2)
Not sure what "four levels, 1, 2" means here. Do you mean "four
levels, 1-4" ... ?
> D= Day (1,2)
> S1= Session ( 1,2)
> Q = Qestion ( 1-to 8)
> Applicants are crossed in Questions, but Applicants nested in Stream,
> nested in Day, nested in session (S1). All variables are a a random factor
You need to know that **with modern mixed-model machinery (e.g. nlme,
lme4 as opposed to aov() in R) it is not in general practical to
estimate random-effects terms for variables with fewer than 5 or 6 levels**.
See e.g. http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#singular-fit
>
> I want to calculate SD for A, S, D, S1 and Q, and their interaction
> .score=dependent variable
>
> I have used the following codes, but it seems they are wrong.
>
> lmer(score~ (1|A)+(1|S)+(1+D)+(1|S1)+(1|Q)+(1|A/S)+1|S/D)+(1|D/S1)+(1|S1/Q),
> R)
(1|S1/D/S/A) gives "Applicants nested in Stream, nested in Day, nested
in session (S1)". As I said above, it would be wiser if possible to use
S1+ (1|S1:D/S/A) (i.e. treat session as a fixed effect).
I would probably handle questions via (1|Q); if each applicant receives
each question no more than once within a session/day/stream combination,
then the S1:D:S:A:Q interaction will be handled by the residual variance
term.
In addition to the problems stated above, many of these terms are
redundant. The nesting syntax (1|A/S) expands to (1|A) + (1|A:S) (i.e.
variability among levels of A, and variability among the interacting
levels of A and S). Fitting a crossed term as compactly as possible
would use (1|A*S), but I think this doesn't actually work: (1|A) + (1|S)
or (1|A:S) or (1|A/S)+(1|S) both describe crossed random effects of A
and S. You may also have the nesting order backwards: (1|A/S) means
"Stream nested within Applicants", not "Applicants nested within Stream".
>
> Linear mixed model fit by REML ['lmerMod']
> Formula: score ~ (1 | A) + (1 | S) + (1 + D) + (1 | S1) + (1 | Q) + (1 |
> A/S) + (1 | S/D) + (1 | D/S1) + (1 | S1/Q)
> Data: R
> REML criterion at convergence: 192.4591
> Random effects:
> Groups Name Std.Dev.
> Q.S1 (Intercept) 0.000e+00
> A (Intercept) 2.383e-01
> S.A (Intercept) 7.692e-01
> A.1 (Intercept) 8.399e-01
> Q (Intercept) 0.000e+00
> S1.D (Intercept) 1.386e-08
> D.S (Intercept) 0.000e+00
> S1 (Intercept) 0.000e+00
> D (Intercept) 9.498e-01
> S (Intercept) 0.000e+00
> S1.1 (Intercept) 0.000e+00
> S.1 (Intercept) 0.000e+00
> Residual 6.722e-01
> Number of obs: 80, groups:
> Q:S1, 16; A, 10; S:A, 10; Q, 8; S1:D, 4; D:S, 4; S1, 2; D, 2; S, 2
> Fixed Effects:
> (Intercept) D
> 1.61458 -0.07292
> convergence code 0; 2 optimizer warnings; 0 lme4 warnings
>
> Very much appreciated for your help.
> looking forward to hearing from you.
> Rose
>
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>
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