Hi, I used DESeq2 to analysis read count data using LRT test.

I have read counts at transcript level and I want to conduct LRT test using multivariate GLM model. (compare full and reduced model)

But my MAplot and dispersion plot do not look like typical plots in the manual. Also the histogram of raw p value have a high peak on 1.

Does it indicate a problem of model fitting? Do I need to discard the low-count transcript first? I'm now using the default independent filtering in DESeq2.

Also how "good" do the MAplot and dispersion plot need to be, in order to claim a properly fitted model?

Or should I use other package to do multivariate GLM? 

Your data has both extremely high dispersions and extremely large fold changes. Both are so large as to be highly implausible in almost any count data set. There is likely either a serious problem with your data or a serious problem with your analysis and data processing.

You might want to explain what kind of data this is (what assay, what species, how many genes, how many reads, etc.) and show the code you used starting from the count data to generate those plots. Then we might be able to suggest where things went wrong.