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Quintana, Fernando A. Newton, Michael A. 
Assessing the Order of Dependence for Partially Exchangeable Binary Data Journal of the American Statistical Association 93,441 (March 1998): 194202. Also: http://www.jstor.org/stable/2669616 Cohort(s): NLSY79 Publisher: American Statistical Association Keyword(s): Data Analysis; Data Quality/Consistency; Employment, Youth; Health/Health Status/SF12 Scale; Markov chain / Markov model; Monte Carlo; Statistical Analysis The problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences. We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new Monte Carlo scheme. Asymptotic tests are also discussed. In particular, we show that the likelihood ratio tests have an asymptotic chisquare distribution, thus generalizing the results of Billingsley (1961) for the particular case of Markov chains. We apply these methods to several data sets, and perform a simulation to study their properties. This article is concerned with the nonparametric statistical analysis of multiple binary sequences, a commonly occurring data structure. One example that we consider comes from dairy science, where each of a number of cows is tested for the presence of a pathogen infection throughout the lactation cycle. Sports statistics provide our second example, in which each of many baseball players produces a sequence of hits/no hits over the course of a season (Albright 1993). A third example comes from the National Longitudinal Survey of Youth (NLSY), in which the employment and health status of a group of young people are monitored yearly by questionnaire (see Borus 1984). It is natural to allow correlation within each binary sequence when formulating models for such data. Among the various approaches, a particularly simple model says that each binary sequence is the realization of a Markov chain having some order of serial dependence. Zerothorder chains correspond to independence, firstorder chains exhibit serial dependence on the most recent binary variable, secondorder chains depend on the most recent pair of variables, and so on. 

Bibliography Citation
Quintana, Fernando A. and Michael A. Newton. "Assessing the Order of Dependence for Partially Exchangeable Binary Data." Journal of the American Statistical Association 93,441 (March 1998): 194202.
