I am trying to run a mixed model on over-dispersed non-integer data. My data are not counts, but are zero-inflated and over dispersed. The variable is distance (how far a gps point is from a central location) and as such looks like: 0.33, 64.73, 5.2 etc. I have been using a quasi-Poisson distribution as I have read that quasi can handle non-integer data (both Poisson and negative binomial cannot). I am using the
glmmPQL function in package MASS as this allows quasi distributions with a random term (the identity of the individual that the gps point comes from).The functions
lmer do not work with a quasi-Poisson distribution. Plotting the residuals indicates a lack of fit of this model.log-transforming the data to try and make it normal before hand also fails (the Shapiro-test for normality is significant). I am unsure how to fix this, as I seemingly have to use a quasi-distribution (link="log") because my data is not counts, non-integer and not normal but there is still overdispersion and lack of fit when using this distribution.
My question therefore is: How to model over-dispersed, non-integer data in a mixed model when quasi-Poisson does not seem to work?
My code so far is:
summary(glmmPQL(distance_from_centroid~Chick.Juv.Adult+Summer_winter, random=~1|markingnumber, family=quasipoisson(link="log"), data=centroid_distances))
Which results in:
Linear mixed-effects model fit by maximum likelihood Data: centroid_distances AIC BIC logLik NA NA NA Random effects: `Formula: ~1 | markingnumber (Intercept) Residual StdDev: 1.157381 2.136811 Variance function: Structure: fixed weights Formula: ~invwt Fixed effects: distance._from_centroid ~ Chick.Juv.Adult + Summer_winter Value Std.Error DF t-value p-value (Intercept) 2.0670095 0.09403952 695 21.980221 0.0000 Chick.Juv.AdultC -0.2945360 0.06686399 695 -4.405002 0.0000 Chick.Juv.AdultJ -0.2005831 0.06727181 695 -2.981682 0.0030 Summer_winterW 0.1207721 0.04324588 695 2.792684 0.0054 Correlation: (Intr) C.J.AC C.J.AJ Chick.Juv.AdultC -0.565 Chick.Juv.AdultJ -0.512 0.736 Summer_winterW -0.267 0.134 0.043 Standardized Within-Group Residuals: Min Q1 Med Q3 Max -2.53759073 -0.48277169 -0.31041612 0.06314122 7.48672836 Number of Observations: 1009 Number of Groups: 311
Which when plotting the residuals gives me: