data tree; input Stand Age $ Tree $ DBH Lichen; cards; 1 Late Aspen 50 1 1 Late Aspen 35 0 1 Late Aspen 28 0 1 Late Aspen 51 1 1 Late Aspen 18 0 1 Late Birch 42 0 1 Late Birch 36 0 1 Late Birch 33 1 1 Late Birch 25 0 1 Late Birch 31 1 1 Late Pine 37 0 1 Late Pine 35 0 1 Late Pine 33 0 1 Late Pine 45 0 1 Late Pine 38 0 1 Late Spruce 24 0 1 Late Spruce 26 0 1 Late Spruce 21 0 1 Late Spruce 19 0 1 Late Spruce 20 1 2 Late Aspen 63 0 2 Late Aspen 77 0 2 Late Aspen 26 0 2 Late Aspen 41 0 2 Late Aspen 57 0 2 Late Birch 39 0 2 Late Birch 34 0 2 Late Birch 52 1 2 Late Birch 37 0 2 Late Birch 35 0 2 Late Pine 58 0 2 Late Pine 39 0 2 Late Pine 38 0 2 Late Pine 49 0 2 Late Pine 33 0 2 Late Spruce 30 1 2 Late Spruce 24 0 2 Late Spruce 54 1 2 Late Spruce 53 1 2 Late Spruce 21 1 3 Late Aspen 42 0 3 Late Aspen 44 1 3 Late Aspen 48 1 3 Late Aspen 33 0 3 Late Aspen 34 0 3 Late Birch 38 0 3 Late Birch 34 0 3 Late Birch 23 1 3 Late Birch 30 0 3 Late Birch 38 1 3 Late Pine 53 0 3 Late Pine 37 0 3 Late Pine 46 0 3 Late Pine 32 0 3 Late Pine 25 0 3 Late Spruce 18 0 3 Late Spruce 21 1 3 Late Spruce 25 1 3 Late Spruce 22 1 3 Late Spruce 26 0 4 Late Aspen 46 0 4 Late Aspen 30 0 4 Late Aspen 66 0 4 Late Aspen 27 0 4 Late Aspen 60 0 4 Late Birch 23 0 4 Late Birch 39 0 4 Late Birch 38 0 4 Late Birch 27 0 4 Late Birch 28 0 4 Late Pine 58 0 4 Late Pine 38 1 4 Late Pine 34 0 4 Late Pine 54 0 4 Late Pine 37 0 4 Late Spruce 30 0 4 Late Spruce 19 0 4 Late Spruce 31 1 4 Late Spruce 21 0 4 Late Spruce 23 0 5 Late Aspen 77 0 5 Late Aspen 52 1 5 Late Aspen 35 0 5 Late Aspen 48 0 5 Late Aspen 50 0 5 Late Birch 37 1 5 Late Birch 32 1 5 Late Birch 26 1 5 Late Birch 25 0 5 Late Birch 26 0 5 Late Pine 43 0 5 Late Pine 33 0 5 Late Pine 40 0 5 Late Pine 41 0 5 Late Pine 49 0 5 Late Spruce 23 0 5 Late Spruce 19 0 5 Late Spruce 20 0 5 Late Spruce 22 1 5 Late Spruce 19 0 6 Late Aspen 37 0 6 Late Aspen 56 0 6 Late Aspen 67 1 6 Late Aspen 67 0 6 Late Aspen 59 0 6 Late Birch 25 0 6 Late Birch 26 0 6 Late Birch 34 0 6 Late Birch 27 0 6 Late Birch 31 1 6 Late Pine 28 0 6 Late Pine 56 0 6 Late Pine 34 0 6 Late Pine 39 0 6 Late Pine 38 1 6 Late Spruce 29 1 6 Late Spruce 28 1 6 Late Spruce 21 1 6 Late Spruce 20 0 6 Late Spruce 23 1 7 Late Aspen 48 0 7 Late Aspen 46 0 7 Late Aspen 51 1 7 Late Aspen 22 0 7 Late Aspen 65 0 7 Late Birch 30 0 7 Late Birch 22 0 7 Late Birch 24 0 7 Late Birch 41 0 7 Late Birch 24 0 7 Late Pine 66 1 7 Late Pine 42 0 7 Late Pine 41 0 7 Late Pine 51 0 7 Late Pine 38 0 7 Late Spruce 23 0 7 Late Spruce 19 0 7 Late Spruce 22 0 7 Late Spruce 37 0 7 Late Spruce 20 1 8 Late Aspen 40 0 8 Late Aspen 34 0 8 Late Aspen 44 0 8 Late Aspen 36 0 8 Late Aspen 49 0 8 Late Birch 21 0 8 Late Birch 20 0 8 Late Birch 31 0 8 Late Birch 42 0 8 Late Birch 26 1 8 Late Pine 64 0 8 Late Pine 41 0 8 Late Pine 46 0 8 Late Pine 49 1 8 Late Pine 59 0 8 Late Spruce 42 1 8 Late Spruce 22 0 8 Late Spruce 25 0 8 Late Spruce 26 0 8 Late Spruce 34 1 9 Late Aspen 40 0 9 Late Aspen 34 0 9 Late Aspen 26 0 9 Late Aspen 35 0 9 Late Aspen 43 0 9 Late Birch 34 0 9 Late Birch 22 0 9 Late Birch 24 0 9 Late Birch 16 0 9 Late Birch 18 0 9 Late Pine 53 0 9 Late Pine 52 0 9 Late Pine 53 0 9 Late Pine 56 0 9 Late Pine 49 0 9 Late Spruce 34 1 9 Late Spruce 32 1 9 Late Spruce 37 0 9 Late Spruce 26 1 9 Late Spruce 18 0 10 Late Aspen 55 0 10 Late Aspen 58 0 10 Late Aspen 44 0 10 Late Aspen 46 1 10 Late Aspen 50 1 10 Late Birch 22 0 10 Late Birch 25 0 10 Late Birch 28 0 10 Late Birch 19 0 10 Late Birch 22 0 10 Late Pine 31 0 10 Late Pine 33 0 10 Late Pine 58 0 10 Late Pine 43 0 10 Late Pine 69 0 10 Late Spruce 17 1 10 Late Spruce 22 1 10 Late Spruce 22 0 10 Late Spruce 41 0 10 Late Spruce 28 0 11 Early Aspen 21 0 11 Early Aspen 37 1 11 Early Aspen 56 0 11 Early Aspen 52 1 11 Early Aspen 32 0 11 Early Birch 36 1 11 Early Birch 19 0 11 Early Birch 18 0 11 Early Birch 59 0 11 Early Birch 18 0 11 Early Pine 32 0 11 Early Pine 33 0 11 Early Pine 36 0 11 Early Pine 41 0 11 Early Pine 42 0 11 Early Spruce 23 0 11 Early Spruce 38 0 11 Early Spruce 43 0 11 Early Spruce 30 0 11 Early Spruce 21 1 12 Early Aspen 24 1 12 Early Aspen 49 0 12 Early Aspen 34 0 12 Early Aspen 38 0 12 Early Aspen 31 1 12 Early Birch 24 0 12 Early Birch 17 1 12 Early Birch 32 1 12 Early Birch 21 0 12 Early Birch 18 1 12 Early Pine 26 1 12 Early Pine 34 0 12 Early Pine 48 0 12 Early Pine 36 0 12 Early Pine 34 0 12 Early Spruce 26 0 12 Early Spruce 32 0 12 Early Spruce 20 1 12 Early Spruce 32 0 12 Early Spruce 21 0 13 Early Aspen 24 0 13 Early Aspen 25 0 13 Early Aspen 41 0 13 Early Aspen 46 0 13 Early Aspen 25 0 13 Early Birch 32 0 13 Early Birch 30 0 13 Early Birch 38 0 13 Early Birch 18 1 13 Early Birch 46 0 13 Early Pine 43 0 13 Early Pine 35 0 13 Early Pine 52 0 13 Early Pine 16 0 13 Early Pine 47 0 13 Early Spruce 22 0 13 Early Spruce 26 0 13 Early Spruce 26 0 13 Early Spruce 25 0 13 Early Spruce 55 0 14 Early Aspen 41 0 14 Early Aspen 42 0 14 Early Aspen 53 1 14 Early Aspen 48 0 14 Early Aspen 51 0 14 Early Birch 29 1 14 Early Birch 32 0 14 Early Birch 24 0 14 Early Birch 37 0 14 Early Birch 34 0 14 Early Pine 60 1 14 Early Pine 51 0 14 Early Pine 31 0 14 Early Pine 41 0 14 Early Pine 52 0 14 Early Spruce 28 0 14 Early Spruce 44 1 14 Early Spruce 30 1 14 Early Spruce 24 0 14 Early Spruce 21 1 15 Early Aspen 39 0 15 Early Aspen 33 0 15 Early Aspen 42 0 15 Early Aspen 37 0 15 Early Aspen 48 0 15 Early Birch 36 0 15 Early Birch 28 0 15 Early Birch 46 0 15 Early Birch 40 0 15 Early Birch 32 0 15 Early Pine 48 0 15 Early Pine 55 0 15 Early Pine 56 0 15 Early Pine 54 0 15 Early Pine 62 0 15 Early Spruce 30 0 15 Early Spruce 30 0 15 Early Spruce 24 0 15 Early Spruce 46 0 15 Early Spruce 19 0 17 Early Aspen 17 1 17 Early Aspen 21 0 17 Early Aspen 15 0 17 Early Aspen 24 0 17 Early Aspen 35 0 17 Early Birch 23 1 17 Early Birch 17 0 17 Early Birch 22 0 17 Early Birch 21 1 17 Early Birch 21 0 17 Early Pine 41 0 17 Early Pine 49 0 17 Early Pine 44 0 17 Early Pine 54 0 17 Early Pine 43 0 17 Early Spruce 23 0 17 Early Spruce 17 0 17 Early Spruce 19 0 17 Early Spruce 23 0 17 Early Spruce 16 0 18 Early Aspen 27 1 18 Early Aspen 27 0 18 Early Aspen 34 1 18 Early Aspen 34 0 18 Early Aspen 37 0 18 Early Birch 23 0 18 Early Birch 27 0 18 Early Birch 34 1 18 Early Birch 19 0 18 Early Birch 35 1 18 Early Pine 41 0 18 Early Pine 42 0 18 Early Pine 35 0 18 Early Pine 23 0 18 Early Pine 34 0 18 Early Spruce 32 0 18 Early Spruce 20 0 18 Early Spruce 27 0 18 Early Spruce 35 0 18 Early Spruce 21 0 20 Early Aspen 30 0 20 Early Aspen 38 0 20 Early Aspen 30 0 20 Early Aspen 22 0 20 Early Aspen 26 0 20 Early Birch 23 1 20 Early Birch 32 0 20 Early Birch 38 1 20 Early Birch 28 0 20 Early Birch 33 0 20 Early Pine 48 1 20 Early Pine 50 0 20 Early Pine 57 1 20 Early Pine 37 0 20 Early Pine 34 0 20 Early Spruce 26 1 20 Early Spruce 22 1 20 Early Spruce 36 0 20 Early Spruce 40 0 20 Early Spruce 55 1 21 Early Aspen 27 0 21 Early Aspen 54 0 21 Early Aspen 48 0 21 Early Aspen 37 1 21 Early Aspen 43 0 21 Early Birch 23 0 21 Early Birch 24 0 21 Early Birch 31 0 21 Early Birch 51 1 21 Early Birch 41 0 21 Early Pine 38 0 21 Early Pine 41 0 21 Early Pine 34 0 21 Early Pine 34 0 21 Early Pine 44 0 21 Early Spruce 22 0 21 Early Spruce 31 0 21 Early Spruce 37 0 21 Early Spruce 32 0 21 Early Spruce 30 0 22 Early Aspen 18 1 22 Early Aspen 54 0 22 Early Aspen 51 1 22 Early Aspen 24 0 22 Early Aspen 36 0 22 Early Birch 37 0 22 Early Birch 29 1 22 Early Birch 21 0 22 Early Birch 29 0 22 Early Birch 19 0 22 Early Pine 35 0 22 Early Pine 23 0 22 Early Pine 38 0 22 Early Pine 32 0 22 Early Pine 36 0 22 Early Spruce 19 0 22 Early Spruce 26 0 22 Early Spruce 30 0 22 Early Spruce 16 0 22 Early Spruce 17 0 23 Old Aspen 44 0 23 Old Aspen 37 0 23 Old Aspen 35 0 23 Old Aspen 54 1 23 Old Aspen 50 0 23 Old Birch 30 0 23 Old Birch 34 1 23 Old Birch 44 1 23 Old Birch 22 1 23 Old Birch 32 0 23 Old Pine 60 0 23 Old Pine 54 0 23 Old Pine 66 1 23 Old Pine 66 1 23 Old Pine 38 1 23 Old Spruce 32 1 23 Old Spruce 21 1 23 Old Spruce 20 0 23 Old Spruce 46 1 23 Old Spruce 25 1 24 Old Aspen 49 1 24 Old Aspen 43 0 24 Old Aspen 45 0 24 Old Aspen 42 0 24 Old Aspen 35 0 24 Old Birch 22 1 24 Old Birch 25 1 24 Old Birch 32 0 24 Old Birch 19 1 24 Old Birch 30 1 24 Old Pine 44 1 24 Old Pine 43 1 24 Old Pine 29 1 24 Old Pine 36 1 24 Old Pine 61 1 24 Old Spruce 41 1 24 Old Spruce 21 0 24 Old Spruce 22 0 24 Old Spruce 27 1 24 Old Spruce 57 1 25 Old Aspen 30 1 25 Old Aspen 23 1 25 Old Aspen 35 0 25 Old Aspen 26 0 25 Old Aspen 29 0 25 Old Birch 23 0 25 Old Birch 31 1 25 Old Birch 36 1 25 Old Birch 24 0 25 Old Birch 29 1 25 Old Pine 39 0 25 Old Pine 24 0 25 Old Pine 42 1 25 Old Pine 40 1 25 Old Pine 34 0 25 Old Spruce 38 1 25 Old Spruce 17 1 25 Old Spruce 25 1 25 Old Spruce 25 1 25 Old Spruce 49 1 26 Old Aspen 43 0 26 Old Aspen 23 0 26 Old Aspen 44 0 26 Old Aspen 43 0 26 Old Aspen 58 1 26 Old Birch 29 0 26 Old Birch 33 1 26 Old Birch 33 1 26 Old Birch 41 0 26 Old Birch 30 1 26 Old Pine 39 1 26 Old Pine 38 1 26 Old Pine 28 1 26 Old Pine 33 1 26 Old Pine 46 1 26 Old Spruce 26 1 26 Old Spruce 31 1 26 Old Spruce 52 1 26 Old Spruce 64 1 26 Old Spruce 23 1 27 Old Aspen 54 1 27 Old Aspen 43 0 27 Old Aspen 33 0 27 Old Aspen 53 0 27 Old Aspen 48 0 27 Old Birch 25 1 27 Old Birch 33 1 27 Old Birch 25 1 27 Old Birch 32 1 27 Old Birch 27 1 27 Old Pine 52 1 27 Old Pine 33 1 27 Old Pine 52 1 27 Old Pine 30 1 27 Old Pine 34 1 27 Old Spruce 44 1 27 Old Spruce 33 1 27 Old Spruce 25 1 27 Old Spruce 32 1 27 Old Spruce 28 1 28 Old Aspen 27 0 28 Old Aspen 45 0 28 Old Aspen 31 0 28 Old Aspen 40 1 28 Old Aspen 43 1 28 Old Birch 40 1 28 Old Birch 28 1 28 Old Birch 26 1 28 Old Birch 36 1 28 Old Birch 37 1 28 Old Pine 29 0 28 Old Pine 39 1 28 Old Pine 45 1 28 Old Pine 37 0 28 Old Pine 43 1 28 Old Spruce 38 1 28 Old Spruce 38 1 28 Old Spruce 43 1 28 Old Spruce 23 0 28 Old Spruce 46 0 29 Old Aspen 34 1 29 Old Aspen 36 1 29 Old Aspen 34 1 29 Old Aspen 28 0 29 Old Aspen 48 1 29 Old Birch 26 1 29 Old Birch 18 1 29 Old Birch 42 1 29 Old Birch 31 1 29 Old Birch 28 1 29 Old Pine 33 0 29 Old Pine 32 1 29 Old Pine 44 1 29 Old Pine 43 0 29 Old Pine 31 1 29 Old Spruce 29 0 29 Old Spruce 22 1 29 Old Spruce 38 1 29 Old Spruce 35 1 29 Old Spruce 31 1 30 Old Aspen 29 0 30 Old Aspen 36 0 30 Old Aspen 32 0 30 Old Aspen 40 1 30 Old Aspen 26 1 30 Old Birch 40 0 30 Old Birch 25 1 30 Old Birch 34 1 30 Old Birch 19 1 30 Old Birch 22 0 30 Old Pine 47 0 30 Old Pine 33 1 30 Old Pine 32 1 30 Old Pine 40 1 30 Old Pine 32 1 30 Old Spruce 46 1 30 Old Spruce 29 1 30 Old Spruce 24 1 30 Old Spruce 31 1 30 Old Spruce 24 0 31 Old Aspen 42 0 31 Old Aspen 45 0 31 Old Aspen 19 0 31 Old Aspen 26 0 31 Old Aspen 22 0 31 Old Birch 37 1 31 Old Birch 23 1 31 Old Birch 19 0 31 Old Birch 18 1 31 Old Birch 25 1 31 Old Pine 31 1 31 Old Pine 27 0 31 Old Pine 31 1 31 Old Pine 34 0 31 Old Pine 37 1 31 Old Spruce 24 1 31 Old Spruce 22 1 31 Old Spruce 28 1 31 Old Spruce 20 1 31 Old Spruce 35 1 32 Old Aspen 46 0 32 Old Aspen 45 0 32 Old Aspen 33 0 32 Old Aspen 43 0 32 Old Aspen 28 0 32 Old Birch 23 1 32 Old Birch 27 1 32 Old Birch 21 1 32 Old Birch 34 1 32 Old Birch 27 1 32 Old Pine 33 0 32 Old Pine 27 1 32 Old Pine 29 1 32 Old Pine 44 1 32 Old Pine 37 1 32 Old Spruce 45 1 32 Old Spruce 41 0 32 Old Spruce 48 1 32 Old Spruce 27 0 32 Old Spruce 37 0 ;run; *Run a first binomial model; proc genmod data=tree ; class tree stand age; model lichen=age tree age*tree dbh/dist=binomial type3 ; run; *There are a few things to be adjusted here. a) the probability of not finding lichen is modelled, it is more convenient to model the probability of lichen. b) The chi-sq/df measure is not given (since we have individual observations), but we would like to have this to be able to check if there is overdispersion. For a) we include descending, for b) we include aggregate; proc genmod data=tree descending ; class tree stand age; model lichen=age tree age*tree dbh/dist=binomial type3 aggregate ; run; *We could look at additional explanatory variables, e.g. that the probability of lichen increases with the AREA. We can do this by including a new variable dbh2 (dbh squared); data tree1; set tree; dbh2=dbh**2; proc genmod data=tree1 descending; class tree stand age; model lichen=age tree age*tree dbh dbh2 /dist=binomial type3 aggregate ; run; *The first model seemed better, we can look at the estimates we get from that; *We can get also lsmeans for all combinations of age and tree. These means are on the log-odds scale; *When compution lsmean dbh (a continous variable) is set to its mean value; proc genmod data=tree descending plots=all; class tree stand age; model lichen=age tree age*tree dbh/dist=binomial type3 aggregate ; lsmeans age*tree /pdiff ilink; run; *Or we can choose at which value dbh should be; proc genmod data=tree descending plots=all; class tree stand age; model lichen=age tree age*tree dbh/dist=binomial type3 aggregate ; lsmeans age*tree /pdiff ilink at dbh=20; ods output diffs=diffs; run; *The same program using GLIMMIX, s is needed to get parameter estimates; proc glimmix data=tree plots=all; class tree stand age; model lichen =age tree age*tree dbh/dist=binomial s; lsmeans age*tree /pdiff ilink at dbh=20; run; *Some useful plots; proc genmod data=tree descending plots=all; class tree stand age; model lichen=age tree age*tree dbh/dist=binomial type3 aggregate ; effectplot interaction; effectplot fit; effectplot slicefit (sliceby=tree plotby=age); run; *The model above is misspecified, since the trees are gathered in stands, i.e. the data collection is hierarchical. To account for this we need to include a random factor stand*age; proc glimmix data=tree ; class tree stand age; model lichen=age tree age*tree dbh/dist=binomial s; random stand*age; run;