# Analysis of mixed data: methods & applications by Alexander R. de Leon, Keumhee Carrière Chough

By Alexander R. de Leon, Keumhee Carrière Chough

"A accomplished resource on combined info research, research of combined facts: tools & functions summarizes the elemental advancements within the box. Case reports are used widely during the ebook to demonstrate fascinating functions from economics, drugs and health and wellbeing, advertising, and genetics. rigorously edited for gentle clarity and seamless transitions among chaptersAll chapters persist with a common Read more...

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Additional resources for Analysis of mixed data: methods & applications

Example text

For a continuous (or at least ordinal) covariate x, the possible splits take the form x ≤ c, where c is a specified cutpoint. For a categorical covariate x, the possible splits take the form x ∈ {c1 , · · · , cl }, where {c1 , · · · , cl } is a subset of the possible values of x. Once the best split is found by scanning through all possible splits, the data is partitioned into two children nodes, a left and a right node. The process is then repeated recursively for each resulting nodes. Typically, a large tree is built and then a right-size subtree is found by a pruning algorithm in order to avoid overfitting.

One aspect of mixed data inference that has received little attention so far is the so-called location hypothesis, for which the construction of reasonable statistical tests remains an important problem in such applications as quality control (de Leon and Carri`ere, 2000) and clinical studπ ,µ µ ), with ies (Afifi and Elashoff, 1969). Consider the GLOM with location parameter Θ = (π µ 1 , · · · ,µ µ S ) as the CS × 1 vector of state means. 4) for some specified Θ 0 . 4) is referred to in the literature as the one-sample location hypothesis, and much work has been done on the case of continuous data.

Another approach to handling mixed data assumes that the discrete variables are coarsely measured versions of unobservable continuous variables called latent variables, and are obtained by partitioning or thresholding the space of the latent variables into non-overlapping intervals. Models for discrete data specified this way were first suggested by Pearson (1904), and they have been further developed over the years (Skrondal and Rabe−Hesketh, 2004). One such model, called the grouped continuous model (GCM) (de Leon, 2005; Anderson and Pemberton, 1985), considers the multivariate normal distribution as the distribution for the latent variables.