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

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).

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

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.

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.

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.

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.