[R] R: lmer specification for random effects: contradictory reults
Benedetta Cesqui
b.cesqui at hsantalucia.it
Mon Nov 25 15:45:30 CET 2013
Dear Thierry,
thank you for the quick reply.
I have only one question about the approach you proposed.
As you suggested, imagine that the model we end up after the model selection
procedure is:
mod2.1 <- lmer(dT_purs ~ T + Z + (1 +T+Z| subject), data =x, REML= FALSE)
According to the common procedures specified in many manuals and recent
papers, if I want to compute the p_values relative to each term, I will
perform a likelihood test, in which the deviance of the (-2LL) of a model
containing the specific term is compared to another model without it.
In the case of the fixed effect terms I have no problem in the
interpretation of the results. Each comparison returns a significance
associated with the estimated coefficient of the term.
Thus in this case:
mod2.2 <- lmer(dT_purs ~ Z + (1 +T+Z|soggetto) , data = x, REML = FALSE)
mod2.3 <- lmer(dT_purs ~ T + (1 +T+Z|soggetto) , data = x, REML = FALSE)
anova(mod2.1, mod2.2)
p_valueT = 3.203e-05
anova(mod2.1, mod2.3)
p_valueZ = 0.001793
What about the p_value relative to the (1+T+Z|subject)?
One option is to compute:
mod2.4 <- lm(dT_purs ~ T + (1 +T+Z|soggetto) , data = x)
and then execute the loklikelihood test as follows:
L0 <-logLik(mod2.4)
L1 <-logLik(mod2.1)
LR <--2*(L1-L0)
pv <- pchisq(LR,2,ncp = 0, lower.tai=FALSE,log.p = FALSE)
However, what can I conclude on the random slopeif it is significant?
With the previouse approach using the model:
mod2 <- lmer(dT_purs ~ T + Z + (1 +T| subject) + (1+ Z| subject), data =x)
The comparison among the models in which the different termd were
included/excluded provided me the following results:
p_valueT = 1.269e-07;
p_valueZ =0.00322
p_valueTS = 0.4277
p_valueZS = 0.005701
I interpreted the ones relative to the random effects as if the subjects
differed not only in their overall responses, but also in the nature of
their response dT_purse values in the different T conditions, but not in the
different Z conditions.
Benedetta
-----Messaggio originale-----
Da: ONKELINX, Thierry [mailto:Thierry.ONKELINX at inbo.be]
Inviato: lunedì 25 novembre 2013 14:48
A: Benedetta Cesqui; r-help at r-project.org
Cc: r-sig-mixed-models at r-project.org
Oggetto: RE: [R] lmer specification for random effects: contradictory reults
Dear Benedetta,
I think you might want (1+T+Z|subject) as random effects rather than
(1+T|subject) + (1 + Z|subject). The latter has two random intercepts per
subject: a recipe for disaster.
Follow-up posts should only go to the mixed models mailing list which I'm
cc'ing.
Best regards,
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be
To call in the statistician after the experiment is done may be no more than
asking him to perform a post-mortem examination: he may be able to say what
the experiment died of.
~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data.
~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
-----Oorspronkelijk bericht-----
Van: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
Namens Benedetta Cesqui
Verzonden: maandag 25 november 2013 11:13
Aan: r-help at r-project.org
Onderwerp: [R] lmer specification for random effects: contradictory reults
Hi All,
I was wondering if someone could help me to solve this issue with lmer.
In order to understand the best mixed effects model to fit my data, I
compared the following options according to the procedures specified in many
papers (i.e. Baayen
<http://www.google.it/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDsQFjAA
&url=http%3A%2F%2Fwww.ualberta.ca%2F~baayen%2Fpublications%2FbaayenDavidsonB
ates.pdf&ei=FhqTUoXuJKKV7Abds4GYBA&usg=AFQjCNFst7GT7mBX7w9lXItJTtELJSKWJg&si
g2=KGA5MHxOvEGwDxf-Gcqi6g&bvm> R.H. et al 2008) Here, dT_purs is the
response variable, T and Z are the fixed effects, and subject is the random
effect. Random and fixed effects are crossed.:
mod0 <- lmer(dT_purs ~ T + Z + (1|subject), data = x)
mod1 <- lmer(dT_purs ~ T + Z + (1 +tempo| subject), data = x)
mod2 <- lmer(dT_purs ~ T + Z + (1 +tempo| subject) + (1+ Z| subject), data =
x)
mod3 <- lmer(dT_purs ~ T * Z + (1 +tempo| subject) + (1+ Z| subject), data =
x)
mod4 <- lmer(dT_purs ~ T * Z + (1| subject), data = x)
anova(mod0, mod1,mod2, mod3, mod4)
Data: x
Models:
mod0: dT_purs ~ T + Z + (1 | subject)
mod4: dT_purs ~ T * Z + (1 | subject )
mod1: dT_purs ~ T + Z + (1 + T| subject)
mod2: dT_purs ~ T + Z + (1 + T| subject ) + (1 + Z | subject)
mod3: dT_purs ~ T * Z + (1 + T| subject) + (1 + Z | subject)
Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
mod0 5 -689.81 -669.46 349.91 -699.81
mod4 6 -689.57 -665.14 350.78 -701.57 1.7532 1 0.185473
mod1 7 -689.12 -660.62 351.56 -703.12 1.5504 1 0.213070
mod2 10 -695.67 -654.97 357.84 -715.67 12.5563 3 0.005701 **
mod3 11 -695.83 -651.05 358.92 -717.83 2.1580 1 0.141825
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
It turns out that mod2 has the right level of complexity for this dataset.
However when I looked at its summary, I got a correlation of -0.87 for the
random effects relative to the T effect and -1 for the random effects
relatively to the Z.
summary(mod2)
Linear mixed model fit by maximum likelihood ['lmerMod']
Formula: dT_purs ~T + Z + (1 + T | subject) + (1 + Z | subject)
Data: x
AIC BIC logLik deviance
-695.6729 -654.9655 357.8364 -715.6729
Random effects:
Groups Name Variance Std.Dev. Corr
subject (Intercept) 0.0032063 0.05662
T 0.0117204 0.10826 -0.87
subject.1 (Intercept) 0.0005673 0.02382
Z 0.0025859 0.05085 1.00
Residual 0.0104551 0.10225
Number of obs: 433, groups: soggetto, 7
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.02489 0.03833 0.650
T 0.52010 0.05905 8.808
Z -0.09019 0.02199 -4.101
Correlation of Fixed Effects:
(Intr) tempo
T -0.901
Z 0.218 -0.026
If I understand correctly what the correlation parameters reported in the
table are, the correlation of 1 means that, for the Z effects the random
intercept is perfectly collinear with the random slope. Thus, we fit the
wrong model. A random intercept only model would have sufficed.
Am I correct?
If so, should I take mod1 (mod1 <- dT_purs ~ T + Z + (1 + T | subject )
instead of mod2 to fit my data?
Why are these results contradictory?
Finally is a correlation value of -0.87 a too high or an acceptable value ?
Thanks for help me in advance!
Best
Benedetta
---
Benedetta Cesqui, Ph.D.
Laboratory of Neuromotor Physiology
IRCCS Fondazione Santa Lucia
Via Ardeatina 306
00179 Rome, Italy
tel: (+39) 06-51501485
fax:(+39) 06-51501482
E_mail: b.cesqui at hsantalucia.it
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