[R-sig-ME] lmer: effects of forcing fixed intercepts and slopes

Steven J. Pierce pierces1 at msu.edu
Wed Nov 7 14:27:44 CET 2012

For good intro coverage of how to use mixed models specifically for
longitudinal data, I recommend Singer & Willett (2003). It's a pretty
reader-friendly book. It doesn’t specifically cover the case of a binary
dependent variable, but that extension isn’t too hard if you already
understand the link between regression and logistic regression. 

Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis:
Modeling change and event occurrence. New York, NY: Oxford University Press.

Below is series of tutorial articles on multilevel modeling (i.e., one
application of mixed models). It's best to read them in the order listed
because each builds on the previous paper in the list. These are written
about cross-sectional analyses, but the foundations for cross-sectional and
longitudinal analyses with mixed models are pretty much the same. Just
remember that observations nested within person is very similar conceptually
to persons nested within neighborhood. The last paper in the series
specifically focuses on logistic variations of these models. 

Merlo, J. (2003). Multilevel analytical approaches in social epidemiology:
Measures of health variation compared with traditional measures of
association. Journal of Epidemiology and Community Health, 57(8), 550-552.

Merlo, J., Chaix, B., Yang, M., Lynch, J., & Råstam, L. (2005). A brief
conceptual tutorial of multilevel analysis in social epidemiology: linking
the statistical concept of clustering to the idea of contextual phenomenon.
Journal of Epidemiology and Community Health, 59(6), 443-449.

Merlo, J., Yang, M., Chaix, B., Lynch, J., & Råstam, L. (2005). A brief
conceptual tutorial on multilevel analysis in social epidemiology:
investigating contextual phenomena in different groups of people. Journal of
Epidemiology and Community Health, 59(9), 729-736.

Merlo, J., Chaix, B., Yang, M., Lynch, J., & Råstam, L. (2005). A brief
conceptual tutorial on multilevel analysis in social epidemiology:
interpreting neighbourhood differences and the effect of neighbourhood
characteristics on individual health. Journal of Epidemiology and Community
Health, 59(12), 1022-1029.
Merlo, J., Chaix, B., Ohlsson, H., Beckman, A., Johnell, K., Hjerpe, P., et
al. (2006). A brief conceptual tutorial of multilevel analysis in social
epidemiology: using measures of clustering in multilevel logistic regression
to investigate contextual phenomena. Journal of Epidemiology and Community
Health, 60(4), 290-297. http://jech.bmj.com/cgi/content/abstract/60/4/290 

As an alternative to a mixed model, you could also consider using GEE: 

Hanley, J. A., Negassa, A., deB. Edwardes, M. D., & Forrester, J. E. (2003).
Statistical analysis of correlated data using generalized estimating
equations: An orientation. American Journal of Epidemiology, 157(4),
364-375. doi: 10.1093/aje/kwf215

Ballinger, G. A. (2004). Using generalized estimating equations for
longitudinal data analysis. Organizational Research Methods, 7(2), 127-150.
doi: 10.1177/1094428104263672  http://orm.sagepub.com/content/7/2/127 

Steven J. Pierce, Ph.D. 
Associate Director 
Center for Statistical Training & Consulting (CSTAT) 
Michigan State University 
Giltner Hall
293 Farm Lane, Room 178 
East Lansing, MI 48824 
Office Phone: (517) 353-9288 
Office Fax: (517) 353-9307 
E-mail: pierces1 at msu.edu 
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: Gjalt-Jorn Peters [mailto:gjalt-jorn at behaviorchange.eu] 
Sent: Tuesday, November 06, 2012 3:42 PM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] lmer: effects of forcing fixed intercepts and slopes

Dear list,

Thierry, great, thank you very much for your quick reply! I will drop 
moment as a random slope, and read up on the different hypotheses that 
are being tested.

I have one more question. Basically, I have no background in multilevel 
(as you may have guessed :-)). The reason I'm 'in over my head' like 
this, is because I basically want to 'use the proper analysis' for my 
data, and the only method is apparently mixed models. "All I want" is 
the simplest' statistically decent, way to test whether cannabis use at 
the second measurement moment is different in the group that received 
that intervention as compared to the group that didn't.

However, when I try to learn about mixed models, the sources I encounter 
approach the modelling practice very differently. They seem to be about 
much more advanced issues; whether random intercepts and slopes should 
be included, and for which variables, etc (to stick to those issues that 
I at least kind of understand). Apparently, either mixed models are only 
used by people who are statistically much more advanced (i.e. there's a 
gap between 'mainstream researchers' and the people who understand and 
use mixed models), or in fact these sources _do_ discuss the same 
things, but in mixed models the terminology just differs a lot from what 
you encounter in more basic statistical textbooks.

I basically have the idea that although my requirements are very basic, 
I have to learn lots of dark arcane issues to be able to do this 
properly. This is kind of 'scary', as, for example, matrix algebra is, 
well, scary :-)

What do people here think of this? Is mixed models just something you 
should avoid unless you're able & willing to really delve into its 
statistical innards?

Again, thank you very much, kind regards,


On 06-11-2012 17:25, ONKELINX, Thierry wrote:
> Dear Gjalt-Jorn,
> Your null model is too complex for your data. Having only one measurement
per participant per moment, you cannot fit a random 'slope' along moment per
participant. Note the perfect correlation in your null model for the nested
random effect.
> Even at the school levels, the amount of data is not that larger and you
end up with near perfect correlations in this random effect. So I would
advise to drop moment as a random slope.
> Don't forget that the summary of a model is testing different hypotheses
than an LRT between two models! You might do some reading on that topic or
get some local statistical advise.
> Best regards,
> Thierry
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> 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-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] Namens Gjalt-Jorn Peters
> Verzonden: dinsdag 6 november 2012 16:23
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: [R-sig-ME] lmer: effects of forcing fixed intercepts and slopes
> Dear all,
> I run into something I don't understand: I update a model with some terms;
none of the terms is significant; but the model suddenly fits A LOT better .
. .
> The background: I am running a model to test a relatively simple
> hypothesis: that an intervention aiming to reduce cannabis use is
effective. It's a repeated measures design where we measured cannabis use of
each student before and after the intervention. In addition to having
repeated measures, students are nested in schools. A simple plot of the
percentage of cannabis users before and after the intervention, in the
control and the intervention groups, is at
http://sciencerep.org/files/7/plot.png (this plot ignores the schools).
> This is the datafile:
> <R CODE>
>     ### Load data
>     dat.long <-
> header=TRUE, sep = "\t");
>     ### Set 'participant' as factor
>     dat.long$participant <- factor(dat.long$id);
>     head(dat.long);
> </R CODE>
> This is what the head looks like:
>     id moment   school cannabisShow gender age usedCannabis_bi participant
> 1  1 before Zuidoost Intervention      2  NA NA           1
> 2  2 before Zuidoost Intervention      2  NA 0           2
> 3  3 before Zuidoost Intervention      1  NA 1           3
> 4  4 before    Noord Intervention     NA  NA NA           4
> 5  5 before    Noord Intervention     NA  NA 1           5
> 6  6 before    Noord Intervention      1  NA NA           6
> 'school' has 8 levels;
> 'moment' has 2 levels ('before' and 'after'); 'cannabisShow' has 2 levels,
'Intervention' and 'Control'; 'usedCannabis_bi' has 2 levels, 0 and 1; and
participants is the participant identifyer.
> I run a null model and a 'real' model, comparing the fit. These are the
formulations I use:
> <R CODE>
>     rep_measures.1.null  <- lmer(formula = usedCannabis_bi ~
>                                  1 + moment + (1 + moment | school /
>                                  family=binomial(link = "logit"),
>     rep_measures.1.model <- update(rep_measures.1.null, .~. +
>     rep_measures.1.null;
>     rep_measures.1.model;
>     anova(rep_measures.1.null, rep_measures.1.model); </R CODE>
> The second model, where I introduce the interaction between measurement
moment and whether participants received the intervention (this should
reflect an effect of the intervention), fits considerably better than the
original model. But, the interaction is not significant. In fact, none of
the fixed effects is - so I added terms to the model, none of these terms
significantly contributes to the prediction of cannabis use, yet the model
fits a lot better.
> This seems to be a paradox. Could anybody maybe explain how this is
> I also looked at the situation where I impose fixed intercepts and slopes
on the participant level (so intercepts and slopes could only vary per
> <R CODE>
>     rep_measures.2.null  <- lmer(formula = usedCannabis_bi ~
>                                  1 + moment + (1 + moment | school),
>                                  family=binomial(link = "logit"),
>     rep_measures.2.model <- update(rep_measures.2.null, .~. +
>     rep_measures.2.null;
>     rep_measures.2.model;
>     anova(rep_measures.2.null, rep_measures.2.model); </R CODE>
> Now the interaction between 'measurement moment' and 'intervention' is
significant, as I expected; but the improvement in fit between the null
model and the 'full model' is much, much smaller.
> This is very counter-intuitive to me - I have the feeling I'm missing
something basic, but I have no idea what. Any help is much appreciated!
> Thank you very much in advance, kind regards,
> Gjalt-Jorn
> PS: the file with the analyses is at
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