Hello,

I'm working with longitudinal data and have some questions regarding the approach and lmer formulation I've used thus far.  Here is a brief background of the data.

I'm evaluating 2 competing hypotheses.

1) marten use (detections/day) of high elevation habitat is seasonal
and/or
2) construction and wind farm operation affects marten use of high elevation habitat.

Marten use of high elevation habitat was monitored for 2 years using remote dataloggers.  Detections/day were recorded for each marten; this the response.    The best lmer model incorporates both seasons and construction periods.  However, these periods have different lengths and overlap (i.e., 3 construction periods are part of the winter season and 2 are part of the summer season).  The parameter estimates of the best fitting model indicate that marten using this habitat seasonally and that the road blasting period negatively affected use; however, marten contribute differently to the data pool, depending on how much of their home range overlaps this habitat.  Each marten were monitored for a minimum of 2 seasons and 3 construction periods.  Further, some were monitored longer, and that is why I've included "marten" as a random effect.  The formula below is by far the best model (according to AICc), compared to evaluating "season" or "construction" alone.

lmer(detections ~ season + construction + (1|marten)...

However, I think that I need to change this formula to incorporate the varying lengths of the seasons and construction periods.  Based on what I've read it seems that the structure of this data fits a partially crossed design in which the subjects (marten) are partially crossed with the context (season and construction period).

I tried these 2 approaches based on what I've read, but I admit... at this point I'm just winging it!

lmer(detections ~ season + construction + (1|season/marten) + (1|construction/marten)...

It seems to work and reflect patterns based on the raw data, but I want to make sure that I'm interpreting it correctly.  I think it reads, I'm interested in the effects of construction and season on the marten detection rate in high elevation habitat with marten nested in both periods and included as a random intercept.  Am I approaching this correctly?

Thanks in advance,

Alexej



I've attached the summary of the original model:  lmer(detections ~ season + construction + (1|season/marten) + (1|construction/marten)... in case anyone is interested in the output.


Generalized linear mixed model fit by the Laplace approximation
Formula: num.obs ~ localseason + constructionperiod + (1 | marten)
   Data: data_std
    AIC    BIC logLik deviance
 152959 153059 -76464   152927
Random effects:
 Groups Name        Variance Std.Dev.
 marten (Intercept) 2.2226   1.4908
Number of obs: 3732, groups: marten, 11

Fixed effects:
                                      Estimate Std. Error z value Pr(>|z|)
(Intercept)                            1.67314    0.44996    3.72 0.000201 ***
localseasonLeaf-off 2                 -0.01759    0.07582   -0.23 0.816588
localseasonLeaf-off 3                  0.25296    0.09920    2.55 0.010775 *
localseasonLeaf-on 1                  -0.88130    0.07292  -12.09  < 2e-16 ***
localseasonLeaf-on 2                  -0.11932    0.08373   -1.43 0.154129
constructionperiodConstruction Lull   0.38271    0.01935   19.78  < 2e-16 ***
constructionperiodOperational 1       1.81074    0.07732   23.42  < 2e-16 ***
constructionperiodOperational 2       1.31072    0.07764   16.88  < 2e-16 ***
constructionperiodOperational 3       1.80926    0.07759   23.32  < 2e-16 ***
constructionperiodOperational 4       0.57012    0.08574    6.65 2.95e-11 ***
constructionperiodOperational 5      -0.62926    0.09219   -6.83 8.75e-12 ***
constructionperiodOperational 6      -0.42147    0.10401   -4.05 5.07e-05 ***
constructionperiodRoad Clearing       0.70419    0.01772   39.74  < 2e-16 ***
constructionperiodRoad Construction  -0.59348    0.07764   -7.64 2.10e-14 ***
constructionperiodTower Construction  0.80382    0.07603   10.57  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
                 (Intr) lclssnLf-f2 lclL-3 lclL-1 lclssnLf-n2 cns2CL cns2O1 cns2O2 cns2O3 cns2O4 cns2O5 cns2O6 cnstrctnprd2RdCl cnstrctnprd2RdCn
lclssnLf-f2       0.000
lclssnLf-f3       0.000  0.764
lclssnLf-n1       0.000  0.962       0.735
lclssnLf-n2       0.000  0.906       0.844  0.871
cnstrctn2CL      -0.021 -0.129      -0.098 -0.134 -0.117
cnstrctn2O1      -0.006 -0.981      -0.749 -0.943 -0.888       0.249
cnstrctn2O2      -0.006 -0.977      -0.746 -0.939 -0.884       0.248  0.992
cnstrctn2O3      -0.006 -0.977      -0.754 -0.940 -0.894       0.248  0.993  0.989
cnstrctn2O4      -0.005 -0.884      -0.824 -0.850 -0.976       0.225  0.898  0.895  0.905
cnstrctn2O5      -0.005 -0.822      -0.906 -0.791 -0.908       0.209  0.835  0.832  0.841  0.913
cnstrctn2O6      -0.005 -0.729      -0.953 -0.701 -0.805       0.185  0.740  0.737  0.745  0.809  0.886
cnstrctnprd2RdCl -0.023  0.000       0.000  0.000  0.000       0.541  0.135  0.134  0.134  0.121  0.113  0.100
cnstrctnprd2RdCn -0.006 -0.903      -0.690 -0.939 -0.818       0.249  0.919  0.915  0.915  0.828  0.770  0.683  0.135
cnstrctn2TC      -0.006 -0.966      -0.738 -0.959 -0.875       0.254  0.983  0.979  0.979  0.886  0.824  0.730  0.137            0.934


Explanatory Variables
-seasons are broke up into 213 and 152 day periods that relate to marten ecology (leaf emergence and senescence) (4 seasons in a 2 year period).
-construction and operational periods consist of 10 periods (5 periods/year that are mirrored in the following year) that vary in length between 42 and 120 days.  They relate to distinct periods associated with wind farm construction and operation (e.g., road clearing, blasting, and wind tower construction).

Response
-detections/day for individual marten


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