[R-sig-ME] Random slope specification with interactions in fixed effects

[Thierry Onkelinx]

Dear Melanie,

Fitting random slopes requires a range of values within each unit. Since
your covariates remain constant within the cluster, you can't estimate the
slope within each cluster. Hence the model should be
Density ~ NDVI*Alteration + NDVI*WinterSeverity + Alteration*WinterSeverity +
(1|Cluster)

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 22 aug 2023 om 15:13 schreef Melanie Dickie <mvezina using ualberta.ca>:

> Hello,
>
> I am attempting to evaluate the influence of two main continuous
> independent variables (“winter severity” aka WinterSeverity and “% habitat
> alteration” aka Alteration), and their interaction, on a continuous
> dependent variable (“density”, measured as #animals/km2). I have reason to
> suspect the impact of these two variables also depends on the underlying
> habitat context (measured using a continuous variable, let’s say the
> Normalized Difference Vegetation Index “NDVI”). From this, my base model
> is:
>
> Density ~ NDVI*Alteration + NDVI*WinterSeverity + Alteration*WinterSeverity
>
> Density is sampled in quadrats, with multiple quadrats clumped together in
> “clusters”; such that the “cluster” is the true sample unit, if you will,
> and the quadrats are replicated samples of each “cluster”.
>
> One complicating twist is that the independent variables are all measured
> at each “cluster”, such that there is no variation in the independent
> variables within each cluster, but there is variation among clusters. Each
> of the quadrats within each cluster have different density values, but the
> same value for winter severity, % habitat alteration, and NDVI.
>
> Putting the twist aside for a moment, my understanding is that I should be
> using a random slope model to gain inference at the cluster level. The
> random effects would allow the covariate effects to vary among clusters and
> the fixed effects would capture the average effect of each covariate across
> clusters. From this, the full specification of the model is (with
> appropriate specification of the family and link):
>
> Density ~ NDVI*Alteration + NDVI*WinterSeverity + Alteration*WinterSeverity
> + ( NDVI*Alteration  |Cluster) + ( NDVI*WinterSeverity  |Cluster) + (
> NDVI*WinterSeverity  |Cluster)
>
> This model, however, appears to be too complex for my data and will not
> converge. To that end, I have also considered the following reduced model
> that does not include the interactions in the random effect structure (this
> model converges):
>
> Density ~ NDVI*Alteration + NDVI*WinterSeverity + Alteration*WinterSeverity
> + (0+NDVI|Cluster) + (0+Alteration|Cluster) + (0+WinterSeverity|Cluster)
>
> I have two main questions:
>
> 1.       For the simplified model, I am unsure of the interpretation of the
> beta coefficients for the fixed-effect interactions if only the independent
> variables with no interactions are specified as random slopes. Do the fixed
> coefficients still yield inferences at the cluster level?
>
> 2.       Is the lack of variation in independent variables within each
> cluster problematic? Is there an alternative way to model this that I am
> missing?
> Thank you for your help,
> Melanie
> --
> Melanie Dickie
> PhD Candidate
>
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>
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