# Is partitioning variance of random and fixed effects in mixed models more sensitive to missing data (rank deficiency)?

I have a follow-up question to my question about modeling the nested crossed design here: (Crossed random effects: how do we model multiple reciprocal transplants in lme4?). We want to partition variance into random and fixed effects with the model we settled on:

modfinheight.group<-lmer(final.height~SOURCE.type+GARDEN.type+SOURCE.type:GARDEN.type+Transplant.group+ (1|Origin.site)+(1|Transplant.site),data=datrmna.finalheight,REML=F)

I can run r2_nakagawa to get total and fixed variance:

r2_nakagawa(modfinheight.group)

# R2 for Mixed Models

Conditional R2: 0.466 Marginal R2: 0.334

and I can run:

rptRfinalheight.group <- rpt(final.height ~ SOURCE.type + GARDEN.type + Transplant.group + (1 | Origin.site) + (1|Transplant.site), grname = c("Origin.site", "Transplant.site", "Fixed"), data = datrmna.finalheight, datatype = "Gaussian", nboot = 1000, npermut = 0, adjusted = FALSE)

Repeatability estimation using the lmm method

Repeatability for Origin.site R = 0.019 SE = 0.019 CI = [0, 0.065] P = 0.0614 [LRT] NA [Permutation]

Repeatability for Transplant.site R = 0.3 SE = 0.126 CI = [0.029, 0.501] P = 5.04e-15 [LRT] NA [Permutation]

Repeatability for Fixed R = 0.24 SE = 0.113 CI = [0.136, 0.56] P = NA [LRT] NA [Permutation] *with this error: boundary (singular) fit: see ?isSingular

But partR2 does not give me estimates for the fixed effects of "SOURCE.type" and "GARDEN.type"

R2_modht6 <- partR2(modfinheight.group, partvars = c("Transplant.group", "SOURCE.type", "GARDEN.type"), R2_type = "marginal", nboot = 100)

fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=21s
fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient

R2_modht6

R2 (marginal) and 95% CI for the full model: R2 CI_lower CI_upper nboot ndf 0.3337 0.2175 0.5662 100 12

Part (semi-partial) R2: Predictor(s) R2 CI_lower CI_upper nboot ndf Model 0.3337 0.2175 0.5662 100 12 Transplant.group 0.2173 0.0639 0.4668 100 9 SOURCE.type 0.0000 0.0000 0.2814 100 12 GARDEN.type 0.0000 0.0000 0.2814 100 12 Transplant.group+SOURCE.type 0.2173 0.0639 0.4668 100 9 Transplant.group+GARDEN.type 0.2173 0.0639 0.4668 100 9 SOURCE.type+GARDEN.type 0.0000 0.0000 0.2814 100 12 Transplant.group+SOURCE.type+GARDEN.type 0.2173 0.0639 0.4668 100 9

Is it the rank deficiency? (sensu @user974 response here: What is rank deficiency, and how to deal with it?) We have a LOT of mortality (see "survivors" inTable below)

Table 1. Locations of origin sites for the three habitat types within each transplant garden group for the 12 sites (used as sources for plant material and as locations of transplants). The number of rhizomes from each site (with range of replicates) and total number of replicates per site are provided, as well as the total number of rhizomes and replicates within the four reciprocal transplants. The total number of surviving plants from each origin site (and number of survivors in beach, marsh and roadside transplant gardens) is also indicated.

This means some combinations have no data for traits like final height: e.g. no data for plants in beach garden in transplant 2, no marsh or roadside plants survived in beach or marsh in Transplant 2).

Please excuse any inappropriateness in posting like this. I'm still new!