Global model call: glm(formula = Resp1 ~ Cat1 + 1, family = gaussian(link = "identity"),
data = myDat1)
---
Model selection table
(Intrc) Cat1 df logLik AICc delta weight
2 20.95 + 4 -339.547 687.5 0.00 1
1 21.79 2 -354.905 713.9 26.42 0
Models ranked by AICc(x) Reporting your best-specified model(s)
1 Reporting your best-specified models
This section is similar regardless of your model structure (e.g. error distribution assumption). The examples below all assume a normal error distribution assumption but you can use the process presented here for models of any structure.
Reporting your best-specified model means reporting the terms - the predictors and any interactions - that are in your model.
It is good practice to present the model along with the results from the model selection. In this way, you can include multiple best-specified models if there is evidence that more than one might be useful. Depending on your hypothesis and results, you will want to present all models within ∆AICc < 2 of the best-specified model, or all models with any Akaike weight, or simply all models.
Remember from the Hypothesis Testing chapter that you can also use the output from dredge() function to report evidence for how you picked the best-specified model.1
Let us take a look at how you do this with our examples:
Example 1: Resp1 ~ Cat1 + 1
Example 1: Resp1 ~ Cat1 + 1
For Example 1, you will report that your best-specified model is Resp1 ~ Cat1 + 1, i.e. that there is evidence that Cat1 explains variability in Resp1. This was chosen as the best-specified model as it had the lowest AICc and the next highest rank model had a ∆AICc of 26.42 (i.e. ∆AICc > 2). The best-specified model had an Akaike weight of 1.
Example 2: Resp2 ~ Cat2 + Cat3 + Cat2:Cat3 + 1
Example 2: Resp2 ~ Cat2 + Cat3 + Cat2:Cat3 + 1
Global model call: glm(formula = Resp2 ~ Cat2 + Cat3 + Cat2:Cat3, family = gaussian(link = "identity"),
data = myDat2)
---
Model selection table
(Int) Ct2 Ct3 Ct2:Ct3 R^2 df logLik AICc delta weight
8 364.9 + + + 0.69800 13 -553.634 1137.5 0.00 0.964
4 354.9 + + 0.62540 7 -564.419 1144.1 6.55 0.036
2 388.5 + 0.55300 5 -573.243 1157.1 19.63 0.000
1 348.3 0.00000 2 -613.508 1231.1 93.64 0.000
3 331.1 + 0.03933 4 -611.502 1231.4 93.92 0.000
Models ranked by AICc(x) For Example 2, you will report that your best-specified model is Resp2 ~ Cat2 + Cat3 + Cat2:Cat3 + 1, i.e. that there is evidence that Cat2 and Cat3 explain variability in Resp2, and that there is an interaction between the effect of Cat2 and Cat3 on your response - i.e. the effect of Cat2 on Resp2 depends on the value of Cat3.
This was chosen as the best-specified model as it had the lowest AICc and the next highest rank model had a ∆AICc of 6.55 (i.e. ∆AICc > 2). The best-specified model had an Akaike weight of 0.964.
Example 3: Resp3 ~ Num4 + 1
Example 3: Resp3 ~ Num4 + 1
Global model call: glm(formula = Resp3 ~ Num4 + 1, family = gaussian(link = "identity"),
data = myDat3)
---
Model selection table
(Intrc) Num4 df logLik AICc delta weight
2 -226.9 260.1 3 -811.080 1628.4 0.00 1
1 2358.0 2 -883.457 1771.0 142.63 0
Models ranked by AICc(x) For Example 3, you will report that your best-specified model is Resp3 ~ Num4 + 1, i.e. that there is evidence that Num4 explains variability in Resp3.
This was chosen as the best-specified model as it had the lowest AICc and the next highest rank model had a ∆AICc of 142.63 (i.e. ∆AICc > 2). The best-specified model had an Akaike weight of 1.
Example 4: Resp4 ~ Cat5 + Num6 + Cat5:Num6 + 1
Example 4: Resp4 ~ Cat5 + Num6 + Cat5:Num6 + 1
Global model call: glm(formula = Resp4 ~ Cat5 + Num6 + Cat5:Num6 + 1, family = gaussian(link = "identity"),
data = myDat4)
---
Model selection table
(Int) Ct5 Nm6 Ct5:Nm6 R^2 df logLik AICc delta weight
8 98.35 + -0.002931 + 0.8557 7 -234.930 485.1 0.00 1
4 92.25 + 0.009650 0.8166 5 -246.915 504.5 19.39 0
2 96.93 + 0.7923 4 -253.133 514.7 29.61 0
3 94.92 0.017780 0.0848 3 -327.278 660.8 175.73 0
1 104.00 0.0000 2 -331.708 667.5 182.46 0
Models ranked by AICc(x) For Example 4, you will report that your best-specified model is Resp4 ~ Cat5 + Num6 + Cat5:Num6 + 1. This model says that there is evidence that Cat5 and Num6 explain variability in Resp4, and that there is an interaction between Cat5 and Num6 - i.e. the effect of Num6 on Resp4 depends on the value of Cat5.
This was chosen as the best-specified model as it had the lowest AICc and the next highest rank model had a ∆AICc of 19.39 (i.e. ∆AICc > 2). The best-specified model had an Akaike weight of 1.
2 Back to Reporting main page
Footnotes
more to come in the section on communicating↩︎