statisticalrethinkin..

12.1. ORDERED CATEGORICAL OUTCOMES 311bCI ~ dnorm(0,10),c(a1,a2,a3,a4,a5,a6) ~ dnorm(0,10)) ,data=d ,start=list(bA=0,bI=0,bC=0,bAI=0,bCI=0,a1=-1.9,a2=-1.2,a3=-0.7,a4=0.2,a5=0.9,a6=1.8) )No new tricks here. e above just adds two interaction terms and two interaction parameters,bAI and bCI.Now let’s compare these three models. You can use coeftab to get a quick comparisonof estimates:coeftab(m11.1,m11.2,m11.3)R code12.9m11.1 m11.2 m11.3a1 -1.92 -2.84 -2.63a2 -1.27 -2.16 -1.94a3 -0.72 -1.57 -1.34a4 0.25 -0.55 -0.31a5 0.89 0.12 0.36a6 1.77 1.02 1.27bA NA -0.71 -0.47bI NA -0.72 -0.28bC NA -0.96 -0.33bAI NA NA -0.45bCI NA NA -1.27nobs 9930 9930 9930Whatever do these estimates mean? e first six rows, from a1 to a6, are just the α intercepts,one for each value below the maximum of “7”. ese really can’t be interpreted on their own,unless you are very used to reading log-odds values.e next 5 rows, from bA to bCI, are the various slope parameters: three main effectsand two interactions. ese are interpretable on their own, to a limited extent. It makessense to ask, first, if they are very far from zero. You can check the standard errors and 95%confidence intervals with precis and verify that all of the slope estimates are quite reliablynegative. Second, all of the slopes are negative, which implies that each factor/interactionreduces the average response. Including action, intention or contact in a story leads peopleto judge it as less morally permissible. But by how much? Remember, these parametersare part of a function defining cumulative log-odds, so they can be interpreted as changesin cumulative log-odds. But unless you are very comfortable thinking about log-odds andcumulative probability densities, that doesn’t help you much. It also doesn’t help that thischange applies to the cumulative log-odds of every value of the response variable, aside fromthe maximum one (which is fixed at cumulative log-odds ∞).So what to do? When in doubt, plot the model’s predictions. Let’s compare these modelsusing AICc:compare( m11.1 , m11.2 , m11.3 , nobs=nrow(d) )R code12.10k AICc w.AICc dAICc