[R-sig-ME] lmer: effects of forcing fixed intercepts and slopes
Gjalt-Jorn Peters
gjalt-jorn at behaviorchange.eu
Wed Nov 7 15:53:02 CET 2012
Dear list,
Thierry, Steven and Seth: thank you so much for your references! These
provide an excellent starting point. Steven, the articles references are
great to get started until I obtained one or more of the books.
Regardless of how hard mixed models will prove, let it never be said
that the community isn't helpful :-)
Again, thank you very much, kind regards,
Gjalt-Jorn
On 07-11-2012 15:22, Seth W. Bigelow wrote:
> Let me slip in a word of praise for Simon Wood's book, 'Generalized Additive
> Models', particularly chapter 6 on mixed models. The man is a genius for
> explaining statistics, and his introduction to mixed models is the clearest
> I've come across. It's canonical for me!
> --Seth
>
>
> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org
> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of ONKELINX,
> Thierry
> Sent: Wednesday, November 07, 2012 4:01 AM
> To: Gjalt-Jorn Peters; r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] lmer: effects of forcing fixed intercepts and slopes
>
> Mixed models are not that scary. I would recommend to read Zuur et al
> (2009). It was written with 'mainstream researchers' (in ecology) in mind.
> It start with simple linear models and gradually adds complexity (glm, gam,
> lmm, glmm, gamm, ...)
>
> @BOOK{ZuurMixedModels,
> title = {{M}ixed {E}ffects {M}odels and {E}xtensions in {E}cology with
> {R}},
> publisher = {Springer New York},
> year = {2009},
> author = {Zuur, Alain F. and Ieno, Elena N. and Walker, Neil J. and
> Saveliev, Anatoly A. and Smith, Graham M.},
> doi = {10.1007/978-0-387-87458-6}
> }
>
> 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-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 21:42
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: 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,
>
> Gjalt-Jorn
>
>
> 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 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-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 <-
>> read.table("http://sciencerep.org/files/7/the%20cannabis%20show%20-%20
>> data%20in%20long%20format.tsv",
>> 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 /
> participant),
>> family=binomial(link = "logit"),
> data=dat.long);
>> rep_measures.1.model <- update(rep_measures.1.null, .~. +
> moment*cannabisShow);
>> 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
> possible?
>> 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
> school):
>> <R CODE>
>> rep_measures.2.null <- lmer(formula = usedCannabis_bi ~
>> 1 + moment + (1 + moment | school),
>> family=binomial(link = "logit"),
> data=dat.long);
>> rep_measures.2.model <- update(rep_measures.2.null, .~. +
> moment*cannabisShow);
>> 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
>> http://sciencerep.org/files/7/the%20cannabis%20show%20-%20analyses%20f
>> or%20mailing%20list.r
>>
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