[R-sig-ME] Specifying Random Effects For Multiple Cross-Level Interactions

[Thierry Onkelinx]

Dear David,

Please don't post in HTML as is can mangle up code and output.

It seems like you have only 2 or 3 observations per site. That amount of
replications per site only allows to fit a random intercept.

Best regards,

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

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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

2016-04-12 17:10 GMT+02:00 David Jones <david.tn.jones op gmail.com>:

> I have a question about cross-level interactions in lmer which is a novice
> one, but I cannot find examples online to address this in lmer because most
> examples only focus on 1 cross-level interaction at a time.
>
> I am trying to look at a model with 4 L1 variables, 4 L2 variables, and a
> cross-level interaction between each respective pair (for 4 total
> interactions). I have tried to specify the models in lmer, but have had
> problems with the models and understanding why the errors occur. I have
> searched these archives, and also used Doug Bates's slides and the lme4
> wiki, among other resources.
>
> As a preface, my sample is small (N=61, 29 clusters). L1 units (Xs) are
> nested under site (between-subjects variables are the Ws). I would prefer
> to use mixed-effects models if possible given precedent in my field. Here
> are the the models I have tried:
>
> For this first model, I get near perfect correlations between each set of
> random intercepts/slopes (from looking at resources, it is probably because
> my model has too many random effects). Syntax for the model as well as the
> output for random effects is below.
>
> model1 <- lmer(y ~ x1 + x2 + x3 + x4 + w1 + w2 + w3 + w4 +
>                    x1:w1 + x2:w2 + x3:w3 + x4:w4 +
>                    (x1 | site) + (x2 | site) + (x3 | site) + (x4 | site),
> data = dataset,
>                  REML=FALSE)
>
> Random effects:
>  Groups      Name          Variance   Std.Dev.   Corr
>  site        (Intercept)   0.000e+00  0.000e+00
>              x1            7.594e-14  2.756e-07  NaN
>  site.1      (Intercept)   9.916e+00  3.149e+00
>              x2            5.444e+01  7.378e+00  1.00
>  site.2      (Intercept)   0.000e+00  0.000e+00
>              x3            1.965e-11  4.433e-06  NaN
>  site.3      (Intercept)   1.262e-01  3.553e-01
>              x4            2.262e+00  1.504e+00  1.00
>  Residual
>
> Given this, I tried a different model with only 1 random intercept and a 1
> random slope for each L1 variable (which are uncorrelated with intercepts
> or each other). This runs (the first model I listed didn't converge for one
> of my DVs; all of these examples have output associated with the same DV).
> But, I often get perfect 0s for the random effects for the slopes (not even
> a very, very small number like 7.2e-10, but rather literally 0.000 for the
> variance and its SD, as if the random slopes are perfectly multicollinear).
> Syntax and output are below.
>
> model2 <- lmer(y ~ x1 + x2 + x3 + x4 + w1 + w2 + w3 + w4 +
>                    x1:y1 + x2:y2 + x3:y3 + x4:y4 +
>                    (1 | site) + (0 + x1 | site) + (0 + x2 | site) + (0 + x3
> | site) + (0 + x4 | site), data = dataset,
>                  REML=FALSE)
>
>
>  Random effects:
>  Groups      Name              Variance     Std.Dev.
>  site            (Intercept)        4.091         2.023
>  site.1         x1                     0.000         0.000
>  site.2         x2                     0.000         0.000
>  site.3         x3                     0.000         0.000
>  site.4         x4                     0.000         0.000
>  Residual                            53.150       7.290
>
> If I specify a model with fewer effects, I do get non-negligible random
> slopes, but the correlation between random effects generally is still
> perfect.
>
> model3 <- lmer(y ~ x1 + x2 + x3 + x4 + w1 + w2 + w3 + w4 +
>                    x1:y1 + x2:y2 + x3:y3 + x4:y4 +
>                    (x1 | site), data = dataset, REML=FALSE)
>
>  Random effects:
>  Groups    Name            Variance   Std.Dev.   Corr
>  site          (Intercept)      10.01       3.164
>                  x1                  55.76       7.467        1.00
>  Residual                        46.04       6.785
>
> Finally, if I tried to let estimate all random effects and let them covary,
> the model won't run R indicates that there are way too many random effects
> to estimate - syntax for this is below:
>
> model3 <- lmer(y ~ x1 + x2 + x3 + x4 + w1 + w2 + w3 + w4 +
>                    x1:y1 + x2:y2 + x3:y3 + x4:y4 +
>                    (1 + x1 + x2 + x3 + x4 | site), data = dataset,
> REML=FALSE)
>
> The main thing that is confusing me is, for each cross level interaction,
> shouldn't I need a random slope for each L1 predictor? My main question
> then is, how should I address this situation?
>
> I recognize there is something I must be doing wrongly as I am new to
> cross-level interactions. I must be specifying redundant intercepts/slopes
> at some point. As secondary questions, what do the multiple intercepts
> represent that were obtained from the first model, and why are there
> multiple listings for site when specifying uncorrelated random effects
> (e.g., site.1, site.2, etc.)?
>
> Many thanks for your input.
>
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>
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