statisticalrethinkin..

12.1. ORDERED CATEGORICAL OUTCOMES 309Take a look at the parameter estimates. ey are just log-odds estimates for the cumulativeprobability of each value. ere is no estimate for the value “7”, because the cumulativeprobability of the maximum value must be 1. I’m going to hold off on plotting the predictionsfrom this model, until we have models with predictor variables to compare it to.Overthinking: Starting values for intercepts. Before moving on to adding predictor variables tothe model, it’s worth commenting on how to get reasonable starting values for the intercepts. In theexample here, when you fit m11.1, I just guessed at some starting values, and it turned out okay. Butyou won’t always get so lucky. Now that we’re working with non-linear models, maximum likelihoodsometimes needs a helping hand to get to the global maximum. If you accidentally pick poor startingvalues for the parameters, you can get either non-sensical estimates or R may fail to find any likelyestimates at all. is can be very frustrating.A good method for picking starting values for the intercepts in an ordered categorical model ofthis kind is to just use the log-odds definition to find them. Here’s an example, in which I computethe implied log-odds of each observable value, using the data.logodds