[R-sig-ME] AIC Comparison for MLM with Different Distributions

[Thierry Onkelinx]

Dear Kate,

If your response variable is an ordered factor, then use the clmm model as
that is one with the most appropriate distribution. All other models are
workarounds. Hence the AIC comparison is not relevant.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op di 3 mrt. 2020 om 23:30 schreef Kate R <kr.gitcode using gmail.com>:

> Hi all,
>
> Thank you in advance for your time and consideration! I am a
> non-mathematically-inclined graduate student in communication just learning
> multilevel modeling.
>
> I am trying to compare the AIC for 5 different models:
>
>
>    1. model.mn5 <- lmer(anxious ~ num.cm + num.pmc + (1|userid), data =
> df,
>    REML = F)
>    2. model.mn5.log <- lmer(log(anxious) ~ num.cm + num.pmc + (1|userid),
>    data = df, REML = F)
>    3. model.mn5.gamma.log <- glmer(anxious ~ num.cm + num.pmc +
> (1|userid),
>    data = df, family = Gamma(link="log"))
>    4. model.mn5.gamma.id <- glmer(anxious ~ num.cm + num.pmc + (1|userid),
>    data = df, family = Gamma(link="identity"))
>    5. model.ord5 <- clmm(anxious ~ num.cm + num.pmc + (1|userid), data =
>    df, na.action = na.omit)
>
> (num.cm is the group mean and num.pmc is the group-mean-centered score of
> the predictor)
>
> Despite many posts on various help forums, I understand that it's possible
> to compare non-nested models with different distributions as long as all
> terms, including constants, are retained (i.e. see Burnham & Anderson, Ch
> 6.7 <https://www.springer.com/gp/book/9780387953649>), but that different
> R
> packages or model classes might handle constants differently or use
> different algorithms (see point 7 <https://robjhyndman.com/hyndsight/aic/
> >),
> thus making it difficult to directly compare AIC values. To avoid
> this non-comparability pitfall, it was suggested in one post to calculate
> your own log-likelihood (though I'm having trouble finding this post
> again).
>
> Please could you help with the following:
>
>    - What is the best practice for comparing the AICs for these 5 models?
>    - What is the R-code for manually calculating the log-likelihood and/or
>    the AIC to retain all terms, including constants?
>    - Can you compare ordinal models (clmm) with the continuous models?
>    - Do you recommend any other methods and/or packages for comparing
>    models with different distributions and/or links?
>
> Many thanks in advance for your time and consideration! I greatly
> appreciate any suggestions.
>
> Kind regards,
> K
>
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>
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