This paper presents a general statistical methodology for the analysis of multivariate categorical data arising from observer reliability studies. The procedure essentially involves the construction of functions of the observed proportions which are directed at the extent to which the observers agree among themselves and the construction of test statistics for hypotheses involving these functions. Tests for interobserver bias are presented in terms of first-order marginal homogeneity and measures of interobserver agreement are developed as generalized kappa-type statistics. These procedures are illustrated with a clinical diagnosis example from the epidemiological literature.

https://www.jstor.org/stable/pdfplus/2529310.pdf

The measurement of observer agreement for categorical data

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

/pdf/fitting-linear-mixed-effects-models-using-lme4-4zzrpoy9lh.pdf

Fitting Linear Mixed-Effects Models Using lme4

The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).

Generalized Linear Models

Using the result that under the null hypothesis of no misspecification an asymptotically efficient estimator must have zero asymptotic covariance with its difference from a consistent but asymptotically inefficient estimator, specification tests are devised for a number of model specifications in econometrics. Local power is calculated for small departures from the null hypothesis. An instrumental variable test as well as tests for a time series cross section model and the simultaneous equation model are presented. An empirical model provides evidence that unobserved individual factors are present which are not orthogonal to the included right-hand-side variable in a common econometric specification of an individual wage equation.

/pdf/specification-tests-in-econometrics-9sg4xr62ii.pdf

Specification Tests in Econometrics

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth

/pdf/simultaneous-inference-in-general-parametric-models-y1lbb202vv.pdf

Shayle R. Searle

Papers

Linear Models