| Spatial point patterns are a unique form of data where locations of points are the focus of interest. Point patterns arise in many fields, but the first uses of statistical methods were in forestry and plant ecology, where a single pattern is considered. While the statistical methodology for a single pattern is fairly well developed, analytical techniques for replicated patterns are sparse.; A mixed model is developed in conjunction with maximum pseudolikelihood and generalized linear mixed modeling by extending Baddeley and Turner's 2000 work on pseudolikelihood for single patterns. An example using the Strauss process, a flexible model which accommodates patterns from extreme inhibition to complete spatial randomness, is investigated in detail. These methods have wider scope, however, and it is shown that they can be used on any Gibbs process whose conditional intensity is log-linear.; Variance components are examined. It is found that empirical estimation agrees well with theoretical results, implying that the model and estimation methods are attributing the different variance components to their correct sources. A new approximation for the variance of the interaction parameter of the Strauss process is derived, and shown to be fairly close to simulation values. Hypothesis testing is developed for the difference of group parameters, including derivation of approximate standard errors. To my knowledge, this is the first non-Monte Carlo test for this type of data.; Four simulation experiments are performed. These concern parameter estimation, variance components (as discussed above), sample size and empty space effects. Fixed and mixed effect models are compared. While mean parameter estimates are similar between the two models, mean absolute deviation, standard deviation, and bias are smaller for the mixed model. The fixed models are prone to outlying solutions, which could bias overall estimates for a set of patterns. The problem intensifies with small sample size. The mixed model does not exhibit this problem due to random shrinkage.; Two sets of data are analyzed. The first concerns developmental biology and is on the spatial distribution of salamander taste buds. The next is pathophyisologic, and is comprised of pyramidal neuronal cell locations in schizophrenic, schizo-affective, and normal subjects. |
