1. Binary Response Harry R. Erwin, PhD School of Computing and Technology University of Sunderland

2. Resources Crawley, MJ (2005) Statistics: An Introduction Using R. Wiley. Freund, RJ, and WJ Wilson (1998) Regression Analysis, Academic Press. Gentle, JE (2002) Elements of Computational Statistics. Springer. Gonick, L., and Woollcott Smith (1993) A Cartoon Guide to Statistics. HarperResource (for fun).

3. Introduction These four demonstration sessions of this class address special types of data: –Counts –Proportions –Survival analysis –Binary responses (this lecture)

4. Binary Response Very common: –dead or alive –occupied or empty –male or female –employed or unemployed Response variable is 0 or 1. R assumes a binomial trial with sample size 1.

5. When to use Binary Response Data Do a binary response analysis only when you have unique values of one or more explanatory variables for each and every individual case. Otherwise lump: aggregate to the point where you have unique values. Either: –Analyse the data as a contingency table using Poisson errors, or –Decide which explanatory variable is key, express the data as proportions, recode as a count of a two-level factor, and assume binomial errors.

6. Applications to Spatial and Time Series Statistics You’re assuming you’re sampling from a spatial point process. The null hypothesis is that events occur uniformly over space and with a Poisson distribution (memory-less) over time. The usual approach is described on the next slide. This addresses both location and rate of events simultaneously. Consider lumping to study the geographic or time-dependent distribution of the event rate separately. The problem is similar to how we model neurone spiking.

7. Modelling Binary Response Single vector with the response variable Use glm with family = binomial Think about a log-log link instead of logit. Fit the usual way. Test significance using  2. Don’t worry about overdispersion. Book example.