[R-sig-ME] Fitting linear mixed model to longitudinal data with very few data points

[David Westergaard]

I agree, but I won't be getting any more data, so I'm trying to find
the least-worst solution, so to speak.

Any suggestions/ideas are most welcome.

Regards,
David

2013/11/24 Steven J. Pierce <pierces1 at msu.edu>:
> You probably need data from a lot more subjects to get good estimates of the
> parameters in that model.
>
>
> Steven J. Pierce, Ph.D.
> Associate Director
> Center for Statistical Training & Consulting (CSTAT)
> Michigan State University
> E-mail: pierces1 at msu.edu
> Web: http://www.cstat.msu.edu
>
> -----Original Message-----
> From: David Westergaard [mailto:david at harsk.dk]
> Sent: Sunday, November 24, 2013 2:55 AM
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] Fitting linear mixed model to longitudinal data with
> very few data points
>
> Hello everyone,
>
> First off, I've posted a similar question to StackExchange
> (http://stats.stackexchange.com/questions/76980/analysis-of-longitudinal-dat
> a-with-very-few-points),
> but I received no answers.
>
> To summarise the data: From 2 subjects, 8 response values were
> measured at time points T0, T1, T2, T3. At T1, subject 1 underwent
> treatment. Subject 1 received no further treatment after T1.
>
> I've reasoned that this is a repeated measures mixed model kind of
> design, so I tried to fit a linear model with random effects, using
> lme4:
>
> lm1 <- lmer(Response ~ Treatment * Timepoint + (1|Subject),
> data=my_data,REML=FALSE)
>
> However, I am not sure if this model is "correct," I have entered time
> points as factorial values, but I am ensure if they should instead be
> numerical values. They are quite spread. On a side note, if I don't
> set REML=FALSE, I get an error "Computed variance-covariance matrix is
> not positive definite" when I try to run "summary(lm1)". I'm guessing
> this may have something to do with my sample size.
>
> I am a bit unsure of how to evaluate the model. The number of data
> points is extremely low. My naive approach was to make an alternative
> model, which does not include treatment:
>
> lm2 <- lmer(Response ~  Timepoint + (1|subject_id), data=test,REML=FALSE)
>
> And do an ANOVA to see which one fits the data better. This is the output:
> anova(lm1,lm2)
>         Df     AIC     BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
> lm2  6   87.12   87.60 -37.561    75.12
> lm1 10 -453.72 -452.93 236.860  -473.72 548.84      4  < 2.2e-16 ***
>
> >From this, can I conclude that lm1 fits the data significantly better,
> and is a reliable model?
>
> What I'm trying to investigate, is:
>
> 1. Is there any observable effect after administering the drug (i.e.
> is the difference between response values significantly greater than
> zero)
> 2. If there is an effect, what is the effect size at each time point
> (i.e. what is the difference between response values)
> 3. How does the effect vary over time
> 4. If there is an effect, is the effect observed from the drug at T1
> still persistant at T3
>
> Any help on this matter is much appreciated.
>
> Regards,
> David
>
>
>