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# How to test for a leading diagonal (home vs. away) effect with binomial data?

I am researching if pathogens are more  or less infectious on the hosts from which they have been isolated.

So there is data on, say 4 pathogen lines (path), tested for %infection success (number diseased (d)/total inoculated(tot))) on all 4 hosts (host) from which they were originally isolated. In the infection matrix, the values on the leading diagonal are pathogens on their own hosts (home=1), while off diagonal are pathogens on novel hosts (home=0).

What model statements in GENMOD would test for a leading diagonal (home vs. away) effect?

Note:

Two approaches I tried using GENMOD give very different siginificance values

Approach 1 -

Get residuals from

Model d/tot = path host /link=logit dist=binom p  r ;

Test home vs. away raw residuals - gives significant leading diagonal effect (P<0.02).

Visual inspection and plotting shows that the 4 leading diagonal resisduals are larger than all except one of the 12 off diagonal values, and the effect "looks real".

Approach 2 -

Compare AIC and likelihood for the above model, with the following more specified model

d/tot = path host home/link=logi dist=binom

Home has a non-siginificant (P=0.23) effect, and comaprison of model with home included gives an AIC improvement of only 0.5, and a likelihood improvement of ca. 0.7.

So approach 2 gives no evidence of a significant leading diagonal, home vs. away effect.

The data:

 Host Path D H home 1 1 12 72 1 1 2 40 36 0 1 3 11 61 0 1 4 50 29 0 2 1 10 105 0 2 2 25 85 1 2 3 3 101 0 2 4 36 78 0 3 1 20 114 0 3 2 60 76 0 3 3 11 117 1 3 4 66 63 0 4 1 20 108 0 4 2 42 76 0 4 3 7 118 0 4 4 54 70 1