Hi everyone,

I'm developing predictive maps of plant species diversity using a data set of richness counts from 668 quadrats divided amongst 109 sites (number of quadrats per site is variable, and depends on site size).

I am modelling richness counts of native and nonnative species using a combination of geoclimatic and air photo-derived land use types, with the hypothesis that higher nonnative species richness will be associated with higher levels of human disturbance, agriculture etc., while the opposite is true for native species richness. Site is used as a random effect to deal with some of the spatial autocorrelation.

>From an original candidate set of 22 predictor variables I kicked out those causing correlations of >0.7 (Spearman), then kicked out a further set that had VIFs >5 (after Zuur 2009), leaving 11 predictor variables which I standardized using z-scores. I found both the native and nonnative count data was better described by a negative binomial distribution than Poisson, and so created a global model using glmmADMB, to which I then applied the Dredge function form MuMIn to get a model set for averaging:

#native sp richness
admb_nr <- glmmadmb(formula=nat_r ~ NR_RD + AG_AR + NR_AG + DEV_AR + SEI_AR + NR_SEI + SLP + NOR + EAST + PA_AR + TMP_RG +  (1|site_code), data=meadow, family="nbinom", zeroInflation = FALSE)
best_subs_n <- dredge(admb_nr, rank = "AIC", trace = TRUE)

Dredge runs fine and yields a model list with coefficients and standard errors that makes sense, but in my R console (I did trace = TRUE and therefore can see each model from Dredge, 2^11 = 2048 models) the warning "Estimated covariance matrix may not be positive definite" appears. The first instance is after the 26th model, then it reappears after every 2 or 3 models from then on. For example:

233 : glmmadmb(formula = nat_r ~ NOR + NR_RD + NR_SEI + PA_AR + 1,
    data = meadow, family = "nbinom", zeroInflation = FALSE)
Estimated covariance matrix may not be positive definite
 0.00017891 0.355147 0.361441 0.37348 0.386851 0.401956 0.446906 0.519341
234 : glmmadmb(formula = nat_r ~ AG_AR + NOR + NR_RD + NR_SEI + PA_AR +
    1, data = meadow, family = "nbinom", zeroInflation = FALSE)
Estimated covariance matrix may not be positive definite
 0.000144364 0.405747 0.412888 0.432029 0.452005 0.493285
Estimated covariance matrix may not be positive definite
 0.000145352 0.403984 0.411032 0.426545 0.432984 0.460366 0.49558

I've read that collinearity can cause this, though I feel like I've addressed that. Though, as Ben discussed in a reply to one of today's messages could it happen if you have variables that are derived from the same layer that could sum to 1? Indeed, AG_AR and DEV_AR are both derived from the same GIS layer, but there are several other polygon types not included in this model so it shouldn't be the problem.

Any insight into what else may cause this warning and what it means for my analysis would me much appreciated. Interestingly, when I run the model and Dredge for the nonnative richness count data I don't get the warning interspersed with each iterative model, but rather it appears after the 2048th about 8 times.

Cheers,

Angela Boag
MSc Candidate
Department of Forest and Conservation Science
University of British Columbia
angela.boag@alumni.ubc.ca

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