Zero-inflated data - ANOVA

#1
Dearest Stat Folk,

I have a visual census dataset (fishes) with lots of zero data. It's essentially a 2-way factorial design (depth, treatment) with 8 replicates of each treatment at the three different depths. The experiment was replicated 5 times. The samples are independent and I used randomized-block design to remove block effects.

I have read about applying delta-lognormal distributions but don't understand how to go about this.

I would greatly appreciate any discussion, suggestions, or help.

Best,
Lance
 
#2
You need to analyze this as factorial randomized block design with count data with poisson distrubution and logit link. Better look on proc GLIMMIX in SAS 9.1.3. or SAS 9.2. Another way is use R with glm.
 

Dason

Ambassador to the humans
#3
Typically a log link is used with Poisson data. It sounds like a reasonable analysis but I'd be wary of making any definitive statements about what a person 'needs' to do without actually seeing the data yourself. For instance they said that there seems to be quite a few 0s. A zero inflated poisson model might be more appropriate?
 
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CB

Super Moderator
#4
Typically a log link is used with Poisson data. It sounds like a reasonable analysis but I'd be wary of making any definitive statements about what a person 'needs' to do without actually seeing the data yourself. For instance they said that there seems to be quite a few 0s. A zero inflated poisson model but be more appropriate?
I agree with this. The Poisson regression assumption of conditional means and variances being equal is not exactly particularly common in real life, unfortunately. Zero-inflated Poisson, negative binomial or zero-inflated negative binomial may be useful. OP - check deviance and/or Pearson chi-square statistics for count-based models you run. If overdispersion (variability in excess of that predicted by the chosen model) is not present, deviance/df and Pearson/df will be close to 1. If deviance/df and Pearson/df are greater than 1, overdispersion is present and you may need a different model.