I know this is quite a basic question and I've checked some related posts on stackoverflow after looking for tutorials/articles explaining what I'm looking for, but so far I did not really get all my points answered.
I did field measurements of different ecological response variables and now have to identify the factors which have a significant influence. For example, I measured bait consumption by soil fauna. I did this on a total of 24 plots (2 regions * 2 elevation levels * 2 expositions (North/South) * 3 plot replicates). Apart from these factors (region/elevation/exposition), I measured some soil properties and extracted climate data from an already existing grid. To reduce the complexity of my soil and climate data, I've done a co-inertia analysis, telling me that soil & climate data do not seem to be significantly correlated. I thus did each a PCA for my soil and my climate data & extracted the first 2 dimensions.
Now, as the residuals of my bait consumption data are not normally distributed, I'm doing a GLM (for other analysis where ND is not violated, I'll do ANOVAs). However, I get myself kind of lost in the process of comparing different GLMs and choosing the most appropriate one.
I started off as follows:
baits.glm0 <- glm(consumption ~ 1, data = baits.stick.means,
family = poisson)
baits.glm1 <- glm(consumption ~ region + exposition +
elevation_level, data = baits.stick.means,
family = poisson)
anova(baits.glm0, baits.glm1, test = "Chisq")
This tells me that including above factors indeed helps in explaining consumption, right. But: how do I continue in adding the other factors (climate_pca1/climate_pca2, soil_pca1/soil_pca2)? I mean there are many different possibilities which factors I add first, which I leave out, do I allow for interactions between e.g. region and exposition, etc ... I can't simply construct different models and look at their AIC, since I get "Inf" for latter, due to the number of factor levels I assume.
So, how would the correct procedure/comparison method be in this case?
Data subset in case it is helpful:
structure(list(stick_number = c(219L, 284L, 62L, 254L, 233L,
187L, 157L, 339L, 57L, 39L, 347L, 340L, 77L, 191L, 321L, 218L,
82L, 153L, 334L, 230L, 194L, 358L, 336L, 78L, 121L, 210L, 224L,
322L, 239L, 83L, 344L, 117L, 204L, 182L, 236L, 306L, 42L, 5L,
112L, 92L, 225L, 32L, 50L, 328L, 359L, 151L, 71L, 30L, 162L,
13L, 111L, 104L, 206L, 296L, 173L, 283L, 228L, 293L, 86L, 256L,
186L, 241L, 264L, 222L, 287L, 143L, 342L, 158L, 266L, 68L, 118L,
156L, 277L, 12L, 8L, 281L, 172L, 259L, 127L, 267L, 6L, 81L, 341L,
327L, 51L, 53L, 31L, 60L, 89L, 308L, 352L, 134L, 64L, 310L, 67L,
302L, 74L, 141L, 268L, 276L), plot_id = c("VSH3", "TSH1", "VNM2",
"VNH2", "VNH1", "VSH1", "TNM2", "TNH2", "VNM1", "VSM3", "TNH3",
"TNH2", "VNM3", "VSH1", "TNH1", "VSH3", "VNM3", "TNM2", "TNH2",
"VNH1", "VSH1", "TNH3", "TNH2", "VNM3", "TSM3", "VSH2", "VSH3",
"TNH1", "VNH1", "VNM3", "TNH2", "TSM2", "VSH2", "VSH1", "VNH1",
"TSH3", "VSM3", "VSM1", "TSM2", "TSM1", "VSH3", "VSM3", "VNM1",
"TNH1", "TNH3", "TNM2", "VNM2", "VSM2", "TNM2", "VSM1", "TSM2",
"TSM1", "VSH2", "TSH2", "TNM3", "TSH1", "VNH1", "TSH2", "VNM3",
"VNH3", "VSH1", "VNH2", "VNH3", "VSH3", "TSH2", "TNM1", "TNH2",
"TNM2", "VNH3", "VNM2", "TSM2", "TNM2", "TSH1", "VSM1", "VSM1",
"TSH1", "TNM3", "VNH3", "TSM3", "VNH3", "VSM1", "VNM3", "TNH2",
"TNH1", "VNM1", "VNM1", "VSM3", "VNM1", "VNM3", "TSH3", "TNH3",
"TSM3", "VNM2", "TSH3", "VNM2", "TSH3", "VNM2", "TNM1", "VNH3",
"TSH1"), site = c("VSH", "TSH", "VNM", "VNH", "VNH", "VSH", "TNM",
"TNH", "VNM", "VSM", "TNH", "TNH", "VNM", "VSH", "TNH", "VSH",
"VNM", "TNM", "TNH", "VNH", "VSH", "TNH", "TNH", "VNM", "TSM",
"VSH", "VSH", "TNH", "VNH", "VNM", "TNH", "TSM", "VSH", "VSH",
"VNH", "TSH", "VSM", "VSM", "TSM", "TSM", "VSH", "VSM", "VNM",
"TNH", "TNH", "TNM", "VNM", "VSM", "TNM", "VSM", "TSM", "TSM",
"VSH", "TSH", "TNM", "TSH", "VNH", "TSH", "VNM", "VNH", "VSH",
"VNH", "VNH", "VSH", "TSH", "TNM", "TNH", "TNM", "VNH", "VNM",
"TSM", "TNM", "TSH", "VSM", "VSM", "TSH", "TNM", "VNH", "TSM",
"VNH", "VSM", "VNM", "TNH", "TNH", "VNM", "VNM", "VSM", "VNM",
"VNM", "TSH", "TNH", "TSM", "VNM", "TSH", "VNM", "TSH", "VNM",
"TNM", "VNH", "TSH"), region = c("valais", "ticino", "valais",
"valais", "valais", "valais", "ticino", "ticino", "valais", "valais",
"ticino", "ticino", "valais", "valais", "ticino", "valais", "valais",
"ticino", "ticino", "valais", "valais", "ticino", "ticino", "valais",
"ticino", "valais", "valais", "ticino", "valais", "valais", "ticino",
"ticino", "valais", "valais", "valais", "ticino", "valais", "valais",
"ticino", "ticino", "valais", "valais", "valais", "ticino", "ticino",
"ticino", "valais", "valais", "ticino", "valais", "ticino", "ticino",
"valais", "ticino", "ticino", "ticino", "valais", "ticino", "valais",
"valais", "valais", "valais", "valais", "valais", "ticino", "ticino",
"ticino", "ticino", "valais", "valais", "ticino", "ticino", "ticino",
"valais", "valais", "ticino", "ticino", "valais", "ticino", "valais",
"valais", "valais", "ticino", "ticino", "valais", "valais", "valais",
"valais", "valais", "ticino", "ticino", "ticino", "valais", "ticino",
"valais", "ticino", "valais", "ticino", "valais", "ticino"),
exposition = c("south", "south", "north", "north", "north",
"south", "north", "north", "north", "south", "north", "north",
"north", "south", "north", "south", "north", "north", "north",
"north", "south", "north", "north", "north", "south", "south",
"south", "north", "north", "north", "north", "south", "south",
"south", "north", "south", "south", "south", "south", "south",
"south", "south", "north", "north", "north", "north", "north",
"south", "north", "south", "south", "south", "south", "south",
"north", "south", "north", "south", "north", "north", "south",
"north", "north", "south", "south", "north", "north", "north",
"north", "north", "south", "north", "south", "south", "south",
"south", "north", "north", "south", "north", "south", "north",
"north", "north", "north", "north", "south", "north", "north",
"south", "north", "south", "north", "south", "north", "south",
"north", "north", "north", "south"), elevation_level = c("high",
"high", "mid", "high", "high", "high", "mid", "high", "mid",
"mid", "high", "high", "mid", "high", "high", "high", "mid",
"mid", "high", "high", "high", "high", "high", "mid", "mid",
"high", "high", "high", "high", "mid", "high", "mid", "high",
"high", "high", "high", "mid", "mid", "mid", "mid", "high",
"mid", "mid", "high", "high", "mid", "mid", "mid", "mid",
"mid", "mid", "mid", "high", "high", "mid", "high", "high",
"high", "mid", "high", "high", "high", "high", "high", "high",
"mid", "high", "mid", "high", "mid", "mid", "mid", "high",
"mid", "mid", "high", "mid", "high", "mid", "high", "mid",
"mid", "high", "high", "mid", "mid", "mid", "mid", "mid",
"high", "high", "mid", "mid", "high", "mid", "high", "mid",
"mid", "high", "high"), climate_pca1 = c(-1.480220428, -1.828098745,
1.770907449, -1.209471355, -1.262109584, -1.575038041, 1.10552354,
-2.332118439, 1.922660686, 2.133086246, -2.251591285, -2.332118439,
1.843690586, -1.575038041, -2.593633876, -1.480220428, 1.843690586,
1.10552354, -2.332118439, -1.262109584, -1.575038041, -2.251591285,
-2.332118439, 1.843690586, 2.081946695, -1.354302896, -1.480220428,
-2.593633876, -1.262109584, 1.843690586, -2.332118439, 1.88376908,
-1.354302896, -1.575038041, -1.262109584, -2.026443343, 2.133086246,
2.129010846, 1.88376908, 1.744163466, -1.480220428, 2.133086246,
1.922660686, -2.593633876, -2.251591285, 1.10552354, 1.770907449,
2.333468357, 1.10552354, 2.129010846, 1.88376908, 1.744163466,
-1.354302896, -1.916565298, 1.208123392, -1.828098745, -1.262109584,
-1.916565298, 1.843690586, -1.027990027, -1.575038041, -1.209471355,
-1.027990027, -1.480220428, -1.916565298, 0.701232975, -2.332118439,
1.10552354, -1.027990027, 1.770907449, 1.88376908, 1.10552354,
-1.828098745, 2.129010846, 2.129010846, -1.828098745, 1.208123392,
-1.027990027, 2.081946695, -1.027990027, 2.129010846, 1.843690586,
-2.332118439, -2.593633876, 1.922660686, 1.922660686, 2.133086246,
1.922660686, 1.843690586, -2.026443343, -2.251591285, 2.081946695,
1.770907449, -2.026443343, 1.770907449, -2.026443343, 1.770907449,
0.701232975, -1.027990027, -1.828098745), climate_pca2 = c(-1.923853312,
-0.509591235, 0.295280113, 0.197102242, -0.42062989, -1.849214144,
2.728812267, 1.351144076, -0.274402516, -1.379004788, 0.77931106,
1.351144076, -0.273885517, -1.849214144, 2.40580586, -1.923853312,
-0.273885517, 2.728812267, 1.351144076, -0.42062989, -1.849214144,
0.77931106, 1.351144076, -0.273885517, -0.018829514, -1.687742087,
-1.923853312, 2.40580586, -0.42062989, -0.273885517, 1.351144076,
0.016797936, -1.687742087, -1.849214144, -0.42062989, -0.733165106,
-1.379004788, -1.358442237, 0.016797936, 0.059349245, -1.923853312,
-1.379004788, -0.274402516, 2.40580586, 0.77931106, 2.728812267,
0.295280113, -1.376450585, 2.728812267, -1.358442237, 0.016797936,
0.059349245, -1.687742087, -0.595492434, 2.621840242, -0.509591235,
-0.42062989, -0.595492434, -0.273885517, -0.670404999, -1.849214144,
0.197102242, -0.670404999, -1.923853312, -0.595492434, 2.615665322,
1.351144076, 2.728812267, -0.670404999, 0.295280113, 0.016797936,
2.728812267, -0.509591235, -1.358442237, -1.358442237, -0.509591235,
2.621840242, -0.670404999, -0.018829514, -0.670404999, -1.358442237,
-0.273885517, 1.351144076, 2.40580586, -0.274402516, -0.274402516,
-1.379004788, -0.274402516, -0.273885517, -0.733165106, 0.77931106,
-0.018829514, 0.295280113, -0.733165106, 0.295280113, -0.733165106,
0.295280113, 2.615665322, -0.670404999, -0.509591235), soil_pca1 = c(-5.56767863419797,
1.95393811095034, -0.260227094874325, -1.61085398656141,
-1.66958542579672, -0.397280823855903, 3.7169854524207, 1.84352513299293,
-0.6551280697025, -6.50320343705425, 2.00291533466174, 1.84352513299293,
-0.620445610945974, -0.397280823855903, 2.42091640839051,
-5.56767863419797, -0.620445610945974, 3.7169854524207, 1.84352513299293,
-1.66958542579672, -0.397280823855903, 2.00291533466174,
1.84352513299293, -0.620445610945974, 0.304033246117126,
-0.84551981325722, -5.56767863419797, 2.42091640839051, -1.66958542579672,
-0.620445610945974, 1.84352513299293, 0.859821441854325,
-0.84551981325722, -0.397280823855903, -1.66958542579672,
2.52191101044192, -6.50320343705425, -4.58332766496856, 0.859821441854325,
1.81674404592665, -5.56767863419797, -6.50320343705425, -0.6551280697025,
2.42091640839051, 2.00291533466174, 3.7169854524207, -0.260227094874325,
-3.61912580538706, 3.7169854524207, -4.58332766496856, 0.859821441854325,
1.81674404592665, -0.84551981325722, 2.72504002601633, 2.85277767098365,
1.95393811095034, -1.66958542579672, 2.72504002601633, -0.620445610945974,
-0.76015927833061, -0.397280823855903, -1.61085398656141,
-0.76015927833061, -5.56767863419797, 2.72504002601633, 4.07392776417628,
1.84352513299293, 3.7169854524207, -0.76015927833061, -0.260227094874325,
0.859821441854325, 3.7169854524207, 1.95393811095034, -4.58332766496856,
-4.58332766496856, 1.95393811095034, 2.85277767098365, -0.76015927833061,
0.304033246117126, -0.76015927833061, -4.58332766496856,
-0.620445610945974, 1.84352513299293, 2.42091640839051, -0.6551280697025,
-0.6551280697025, -6.50320343705425, -0.6551280697025, -0.620445610945974,
2.52191101044192, 2.00291533466174, 0.304033246117126, -0.260227094874325,
2.52191101044192, -0.260227094874325, 2.52191101044192, -0.260227094874325,
4.07392776417628, -0.76015927833061, 1.95393811095034), soil_pca2 = c(-1.20094768276013,
-0.81049387016335, 2.4943393252285, 1.57423563197107, 1.44861597315028,
2.2610844297929, -0.297648866553386, -2.38340996245776, 2.40878156685994,
-2.3823643056849, -2.6231255135526, -2.38340996245776, 2.23860580682454,
2.2610844297929, -1.9422384338934, -1.20094768276013, 2.23860580682454,
-0.297648866553386, -2.38340996245776, 1.44861597315028,
2.2610844297929, -2.6231255135526, -2.38340996245776, 2.23860580682454,
-0.828230153957865, 1.8842217721005, -1.20094768276013, -1.9422384338934,
1.44861597315028, 2.23860580682454, -2.38340996245776, 1.69610095222163,
1.8842217721005, 2.2610844297929, 1.44861597315028, 0.219212508989128,
-2.3823643056849, -0.56282968564021, 1.69610095222163, -0.404846537234961,
-1.20094768276013, -2.3823643056849, 2.40878156685994, -1.9422384338934,
-2.6231255135526, -0.297648866553386, 2.4943393252285, -2.50519920681956,
-0.297648866553386, -0.56282968564021, 1.69610095222163,
-0.404846537234961, 1.8842217721005, -0.561939092870071,
-1.23645258422661, -0.81049387016335, 1.44861597315028, -0.561939092870071,
2.23860580682454, 1.62581106228919, 2.2610844297929, 1.57423563197107,
1.62581106228919, -1.20094768276013, -0.561939092870071,
-0.111283133612885, -2.38340996245776, -0.297648866553386,
1.62581106228919, 2.4943393252285, 1.69610095222163, -0.297648866553386,
-0.81049387016335, -0.56282968564021, -0.56282968564021,
-0.81049387016335, -1.23645258422661, 1.62581106228919, -0.828230153957865,
1.62581106228919, -0.56282968564021, 2.23860580682454, -2.38340996245776,
-1.9422384338934, 2.40878156685994, 2.40878156685994, -2.3823643056849,
2.40878156685994, 2.23860580682454, 0.219212508989128, -2.6231255135526,
-0.828230153957865, 2.4943393252285, 0.219212508989128, 2.4943393252285,
0.219212508989128, 2.4943393252285, -0.111283133612885, 1.62581106228919,
-0.81049387016335), exposure_days = c(21, 19, 20, 20, 20,
21, 20, 20, 20, 19, 20, 20, 20, 21, 20, 21, 20, 20, 20, 20,
21, 20, 20, 20, 19, 21, 21, 20, 20, 20, 20, 19, 21, 21, 20,
19, 19, 19, 19, 19, 21, 19, 20, 20, 20, 20, 20, 19, 20, 19,
19, 19, 21, 19, 20, 19, 20, 19, 20, 20, 21, 20, 20, 21, 19,
20, 20, 20, 20, 20, 19, 20, 19, 19, 19, 19, 20, 20, 19, 20,
19, 20, 20, 20, 20, 20, 19, 20, 20, 19, 20, 19, 20, 19, 20,
19, 20, 20, 20, 19), consumption = c(0.065625, 0, 0.3125,
0.34375, 0.175, 0.184375, 0.453125, 0.0192307692307692, 0.271875,
0, 0.00625, 0, 0.896875, 0.25625, 0.3125, 0.021875, 0.265625,
0.46875, 0.0375, 0.421875, 0.121875, 0.159375, 0.181818181818182,
0.1875, 0.09375, 0.0625, 0.096875, 0.583333333333333, 0.0625,
0.140625, 0.1875, 0, 0.00625, 0.5875, 0.1625, 0.5625, 0.078125,
0, 0, 0, 0.015625, 0, 0.490625, 0.533333333333333, 0.246875,
0.546875, 0.3125, 0.209375, 0.225, 0, 0, 0.375, 0.08125,
0.265625, 0.178125, 0.2, 0.1, 0.109375, 0.590625, 0.065625,
0.0375, 0.1375, 0.115625, 0.13125, 0.53125, 0.4375, 0.21875,
0.171875, 0.06875, 0.1875, 0.0625, 0.65625, 0, 0, 0.00625,
0, 0.225, 0.153125, 0.171875, 0.10625, 0, 0.596875, 0.125,
0.190909090909091, 0.496875, 0.88125, 0.00625, 0.615625,
0.725, 0.5625, 0.146875, 0.046875, 0.31875, 0.1, 0.646875,
0.265625, 0.578125, 0.5, 0.075, 0.03125), cons_transf = c(0.25617376914899,
0, 0.559016994374947, 0.586301969977929, 0.418330013267038,
0.429389100932942, 0.673145600891813, 0.138675049056307,
0.521416340365355, 0, 0.0790569415042095, 0, 0.947034846243791,
0.506211418282915, 0.559016994374947, 0.14790199457749, 0.515388203202208,
0.684653196881458, 0.193649167310371, 0.649519052838329,
0.349106001094224, 0.399217985566783, 0.426401432711221,
0.433012701892219, 0.306186217847897, 0.25, 0.311247489949718,
0.763762615825973, 0.25, 0.375, 0.433012701892219, 0, 0.0790569415042095,
0.766485485837795, 0.403112887414928, 0.75, 0.279508497187474,
0, 0, 0, 0.125, 0, 0.700446286306095, 0.730296743340221,
0.496865172858795, 0.739509972887452, 0.559016994374947,
0.457575130443078, 0.474341649025257, 0, 0, 0.612372435695794,
0.285043856274785, 0.515388203202208, 0.422048575403353,
0.447213595499958, 0.316227766016838, 0.330718913883074,
0.76852130744697, 0.25617376914899, 0.193649167310371, 0.370809924354783,
0.340036762718386, 0.362284418654736, 0.728868986855663,
0.661437827766148, 0.467707173346743, 0.414578098794425,
0.262202212042538, 0.433012701892219, 0.25, 0.810092587300983,
0, 0, 0.0790569415042095, 0, 0.474341649025257, 0.391311896062463,
0.414578098794425, 0.325960120260132, 0, 0.772576857018122,
0.353553390593274, 0.436931448752651, 0.704893608993584,
0.938749167775929, 0.0790569415042095, 0.784617741323761,
0.85146931829632, 0.75, 0.383242742918897, 0.21650635094611,
0.564579489531811, 0.316227766016838, 0.804285397107271,
0.515388203202208, 0.760345316287277, 0.707106781186548,
0.273861278752583, 0.176776695296637), cons_transf2 = c(0.0635614814897446,
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