[R] hierarchical mixture modelling

[Mike Lawrence]

Hi folks,

I have circular data that I'd like to model as a mixture of a uniform
and a Von Mises centered on zero. The data are from 2 groups of human
participants, where each participant is measured repeatedly within
each of several conditions. So, the data frame would look something
like:

########
    design = expand.grid(
        person = 1:20
        , variable1 = 1:2
        , variable2 = 1:3
        , repetition = 1:100
    )
    design$group = design$person %% 2
########

where each row would have a data point.

Now, I know how to fit the mixture of a uniform and Von Mises to each
individual cell of the data independently using the EM algorithm,
yielding estimates of the mixture proportion and Von Mises
concentration per cell. However, I of course want to assess the degree
to which the group and other variables in the design affect these
model parameters, and at least in the case of the proportion estimate,
I'm uncomfortable submitting the raw proportion to a test that is
going to assume Gaussian error (eg. ANOVA, or lmer(...,
family=gaussian)). I'm aware that lmer lets one specify non-gaussian
links, but as I understand it, if I wanted to, say, specify the
binomial link (which seems appropriate for a proportion), lmer wants
the data to be the raw 1's and 0's, not the proportion estimate
obtained from EM.

I've heard that there are hierarchical mixture modelling methods out
there (possibly Bayesian hierarchical mixture modelling) that might
let me achieve model fitting and inference in one step (eg. model the
mixture and influence on each parameter from the between and
within-person variables, and treating people as random effects), but
I'm having trouble tacking down instructions on how to do this.

Any pointers would be greatly appreciated!

Cheers,

Mike

--
Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

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~ Certainty is folly... I think. ~