Modelling ordinal responses from co-twin control studies

The co-twin control design has been widely used in studying the effects of environmental factors on the development of diseases. For binary outcomes that arise from co-twin control studies, the conditional likelihood method is commonly used. This approach, however, does not readily extend to ordinal response data because the standard conditional likelihood does not exist for cumulative logit or proportional odds models. In this paper, we investigate the applicability of the random-effects and GEE approaches in analysing ordinal response data from co-twin control studies. Using both approaches, we re-analyse data from a co-twin control study of the impact of military services during the Vietnam era on post-traumatic stress disorders (PTSD). The ordinal models have considerably increased power in detecting the effects of exposure when compared to the analyses using a dichotomized response. We discuss the interpretation of the estimates from GEE and random-effect models in the context of the twin data.     

Refined crystal structure of methylamine dehydrogenase from Paracoccus denitrificans at 1.75 A resolution

We extend the random intercept logistic model to accommodate negative intracluster correlations for bivariate binary response data. This approach assumes a single random effect per cluster, but entails separate affine transformations of this random effect for the two responses of the pair. We show this approach works for two data sets and a simulation, whereas other mixed effects approaches fail. The two data sets are from a crossover trial and a developmental toxicity study of the effects of chemical exposure on malformation risk among rat pups. Comparisons are made with the conditional likelihood approach and with generalized estimating equations estimation of the population-averaged logit model. Simulations show the conditional likelihood approach does not perform well for moderate to strong negative correlations, as a positive intracluster correlation is assumed. The proposed mixed effects approach appears to be slightly more conservative than the population-averaged approach with respect to coverage of confidence intervals. Nonetheless, the statistical literature suggests that mixed effects models provide information in addition to that provided by population-averaged models under scientific contexts such as crossover trials. Extensions to trivariate and higher-dimensional responses also are addressed. However, such extensions require certain constraints on the correlation structure.     

The detection of residual serial correlation in linear mixed models

Diggle (1988) described how the empirical semi-variogram of ordinary least squares residuals can be used to suggest an appropriate serial correlation structure in stationary linear mixed models. In this paper, this approach is extended to non-stationary models which include random effects other than intercepts, and will be applied to prostate cancer data, taken from the Baltimore Longitudinal Study of Aging. A simulation study demonstrates the effectiveness of this extended variogram for improving the covariance structure of the linear mixed model used to describe the prostate data.     

Using Multilevel Models to Analyze Couple and Family Treatment Data: Basic and Advanced Issues.

Couple and family treatment data present particular challenges to statistical analyses. Partners and family members tend to be more similar to one another than to other individuals, which raises interesting possibilities in the data analysis but also causes significant problems with classical, statistical methods. The present article presents multilevel models (also called hierarchical linear models, mixed-effects models, or random coefficient models) as a flexible analytic approach to couple and family longitudinal data. The article reviews basic properties of multilevel models but focuses primarily on 3 important extensions: missing data, power and sample size, and alternative representations of couple data. Information is presented as a tutorial, with a Web appendix providing datasets with SPSS and R code to reproduce the examples. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Developing Regression Models for Predicting Pan Evaporation from Climatic Data—A Comparison of Multiple Least-Squares, Principal Components, and Partial Least-Squares Approaches

Regression models for predicting daily pan evaporation depths from climatic data were developed using three multivariate approaches: multiple least-squares regression (MLR), principal components regression (PCR), and partial least-squares (PLS) regression. The objective was to compare the prediction accuracies of regression models developed by these three approaches using historical climatic datasets of four Indian sites that are located in distinctly different climatic regimes. In all cases (three approaches applied to four climatic datasets), regression models were developed using a part of the data and subsequently validated with the remaining data. Results indicated that although performances of the regression models varied from one climate to another, more or less similar prediction accuracies were obtained by all three approaches, and it was difficult to identify the best approach based on performance statistics. However, the final forms of the regression models developed by the three approaches differed substantially from one another. In all cases, the models derived using PLS contained the smallest number of predictor variables; between two to three out of a possible maximum of six predictor variables. The MLR approach yielded models with three to six predictor variables, and PCR models included all six predictor variables. This implies that the PLS regression models are the most parsimonious in terms of input data required for estimating epan from climate variables, and yet yield predictions that are almost as accurate as the more data-intensive MLR and PCR models.     

Continuous versus discrete information processing: Modeling accumulation of partial information.

Comments on D. E. Meyer and colleagues' (see record 1988-28535-001) new technique for examining the time course of information processing, which is a variant of the response signal procedure: On some trials Ss are presented with a signal that requires them to respond, whereas on other trials they respond normally. The accuracy of guesses based on partial information can be determined by using the data from the regular trials and a simple race model to remove the contribution of fast-finishing regular trials from signal trial data. This analysis shows that the accuracy of guesses is relatively low and is either approximately constant or grows slowly over the time course of retrieval. Myers et al argue that this pattern of results rules out most continuous models of information processing. But the analyses presented in the present article show that this pattern is consistent with several stochastic RT models: the simple random walk, the runs, and the continuous diffusion models. The diffusion model is assessed with data from a new experiment using the study–test recognition memory procedure. Fitting the diffusion model to the data from regular trials fixes all parameters of the model except one (the signal encoding and decision parameter). With this one free parameter, the model predicts the observed guessing accuracy. It is concluded that the results obtained from Meyer and colleagues' new technique give qualitative support to some stochastic models and quantitative support to the continuous diffusion model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mixed effects logistic regression models for longitudinal binary response data with informative drop-out

A shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop-out. The model consists of observed longitudinal and missing response components that share random effects parameters. To our knowledge, this is the first presentation of such a model for longitudinal binary response data. Comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations. The naive mixed effects logit model that does not account for informative drop-out is also compared. The simulation-based differences among the models with respect to coverage of confidence intervals, bias, and mean squared error (MSE) depend on at least two factors: whether an effect is a between- or within-subject effect and the amount of between-subject variation as exhibited by variance components of the random effects distributions. When the shared parameter model holds, the approximate conditional model provides confidence intervals with good coverage for within-cluster factors but not for between-cluster factors. The converse is true for the naive model. Under a different drop-out mechanism, when the probability of drop-out is dependent only on the current unobserved observation, all three models behave similarly by providing between-subject confidence intervals with good coverage and comparable MSE and bias but poor within-subject confidence intervals, MSE, and bias. The naive model does more poorly with respect to the within-subject effects than do the shared parameter and approximate conditional models. The data analysis, which entails a comparison of two pain relievers and a placebo with respect to pain relief, conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome-driven drop-out process. This comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data.     

Methodological advances in family psychology research: Introduction to the special section.

This article introduces a special section in the Journal of Family Psychology on methodological advances in family psychology research. The need for innovative methodologies to capture the richness and complexity of family relationships and to advance the field is discussed. Articles that address the application of mathematical modeling of couple interactions, methods for analyzing sequential observational data, the application of multivariate analysis of variance and confirmatory factor analysis, the application of hierarchical linear modeling, and the use of experimental methods for the study of family process are included in the special section. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Stochastic model of self-regulation decision making exemplified by decisions concerning hypoglycemia.

The following sequence—internal condition → symptom perception → appraisal → decision—models various symptom-based self-regulation processes. A formal mathematical model describes the first three steps by continuous variables and the decisions at the fourth step by binary variables. The stochastic transitions between the sequential steps are quantified by transition probabilities. The model is illustrated by blood glucose level estimation and detection and treatment of hypoglycemia in 78 patients with insulin-dependent diabetes mellitus. These patients made 50 to 70 data collection trials over 3 to 4 weeks recording perceived symptoms, cognitive-motor performance, subjective estimates of blood glucose, decisions about treatment of hypoglycemia, and driving. A statistical estimation of the model's parameters demonstrates the utility of this approach for understanding the awareness, detection, and treatment of hypoglycemia as a process of symptom-based decision making. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Intraclass correlation for two-by-two tables under three sampling designs

Several sampling designs for assessing agreement between two binary classifications on each of n subjects lead to data arrayed in a four-fold table. Following Kraemer's (1979, Psychometrika 44, 461-472) approach, population models are described for binary data analogous to quantitative data models for a one-way random design, a two-way mixed design, and a two-way random design. For each of these models, parameters representing intraclass correlation are defined, and two estimators are proposed, one from constructing ANOVA-type tables for binary data, and one by the method of maximum likelihood. The maximum likelihood estimator of intraclass correlation for the two-way mixed design is the same as the phi coefficient (Chedzoy, 1985, in Encyclopedia of Statistical Sciences, Vol. 6, New York: Wiley). For moderately large samples, the ANOVA estimator for the two-way random design approximates Cohen's (1960, Psychological Measurement 20, 37-46) kappa statistic. Comparisons among the estimators indicate very little difference in values for tables with marginal symmetry. Differences among the estimators increase with increasing marginal asymmetry, and with average prevalence approaching .50.     

Multipoint oligogenic linkage analysis of quantitative traits

We present an overview of pedigree-based variance component linkage methods and discuss their extension to oligogenic inheritance. As an example, oligogenic linkage analyses were performed using the quantitative trait Q4 from the GAW10 simulated data set. A strategy involving sequential oligogenic analyses was found to have increased power to detect the three quantitative trait loci (QTL) influencing Q4 when compared to the classical marginal approach of requiring each locus to have a lod score > or = 3. However, it is shown that requiring conditional lod scores > or = 3 in the sequential analyses may be overly conservative and alternative criteria for the acceptance of multilocus models are discussed.     

Gibbs sampler for the logistic model in the analysis of longitudinal binary data

Logistic mixed-effects models constitute a natural framework to study longitudinal binary response variables when the question addressed with the data is related to covariate effects within persons. However, the computations of the likelihoods are generally tedious and require the resolution of integrals which have no analytical solution. In this paper, we study a logistic mixed-effects model in a Bayesian framework and use the Gibbs sampler to overcome the current computational limitations. From a study of side-effects occurring during plasma exchanges, we explore the issues of bayesian formulation, model parametrization, choice of the prior distributions, diagnosing convergence, comparison between models and model adequacy. Finally, we show that a Bayesian random-effects model is useful to facilitate prediction.     

Hierarchical modeling of sequential behavioral data: An empirical Bayesian approach.

The authors review the common methods for measuring strength of contingency between 2 behaviors in a behavioral sequence, the binomial z score and the adjusted cell residual, and point out a number of limitations of these approaches. They present a new approach using log odds ratios and empirical Bayes estimation in the context of hierarchical modeling, an approach not constrained by these limitations. A series of hierarchical models is presented to test the stationarity of behavioral sequences, the homogeneity of sequences across a sample of episodes, and whether covariates can account for variation in sequences across the sample. These models are applied to observational data taken from a study of the behavioral interactions of 254 couples to illustrate their use. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Level A in vivo-in vitro correlation: nonlinear models and statistical methodology

Some new nonlinear models for the relationship between the fraction of drug dose dissolved (absorbed) in vivo and that dissolved in vitro are described. The models are empirical in nature and are generalizations of the linear model that, at present, is the most commonly used model. The modeling approach is based on considering the time at which a drug molecule goes into solution (in vitro or in vivo) to be a random variable and relating the distribution functions using proportional odds, proportional hazards, and proportional reversed hazards models. The models are further extended by allowing the parameter that relates in vivo and in vitro to be a function of time. A statistical model for the data is developed and used as the basis for a statistical methodology for fitting these models. The methods are shown to be generalized linear mixed effects model (GLMM) methods. The models are fitted to some data sets, and the results demonstrate that these models have potential.     

Adhesive characteristics of type II pneumocyte subpopulations from saline- and silica-treated rats

OBJECTIVES: Using a community-based sample of currently depressed subjects, this research modeled the joint decision to seek depression treatment and choice of provider sector (primary care or specialty mental health). The objective was to identify those subject-specific case-mix factors and those provider sector-specific access measures that significantly impacted this joint decision. METHODS: A community-based sample of 435 Arkansans with current depression symptoms was compiled using random digit dialing and the Burnam depression screener. Study subjects were administered baseline and 6-month follow-up surveys. All medical, pharmaceutical, and insurance records were collected and abstracted to verify service use and depression treatment. Three discrete choice model specifications were tested: sequential binary logit models, a multinomial logit model, and a nested logit model. The nested logit model makes less restrictive assumptions about the patterns of substitution across treatment alternatives than the other model specifications. RESULTS: In the 6 months after baseline, 73.3% of the sample did not seek depression treatment, 18.9% sought care from a primary care provider, and 7.8% sought care from a mental health specialist. A likelihood ratio test identified the nested logit model as the preferred model specification (chi 2 < or = 0.05), indicating that the expected maximum utility of sector choice significantly affects the decision to seek treatment. Provider sector-specific access measures (e.g., insurance coverage and availability) significantly impacted sector choice and, thus, the decision to seek treatment. Subject-specific case-mix factors (e.g., age, gender, employment status, depression severity, and psychiatric comorbidity) significantly affected the decision to seek treatment. CONCLUSIONS: Sector-specific access measures significantly impact both provider sector choice and the decision to seek treatment. Because the primary care and specialty care treatment alternatives were more substitutable with one another than with the no treatment option, changes in access affected sector choice more than the decision to seek treatment.     

Propensity Score Estimation With Boosted Regression for Evaluating Causal Effects in Observational Studies.

Causal effect modeling with naturalistic rather than experimental data is challenging. In observational studies participants in different treatment conditions may also differ on pretreatment characteristics that influence outcomes. Propensity score methods can theoretically eliminate these confounds for all observed covariates, but accurate estimation of propensity scores is impeded by large numbers of covariates, uncertain functional forms for their associations with treatment selection, and other problems. This article demonstrates that boosting, a modern statistical technique, can overcome many of these obstacles. The authors illustrate this approach with a study of adolescent probationers in substance abuse treatment programs. Propensity score weights estimated using boosting eliminate most pretreatment group differences and substantially alter the apparent relative effects of adolescent substance abuse treatment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables.

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location submodel link function is the logit and thereby analogous to logistic regression, whereas the dispersion submodel is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software. (PsycINFO Database Record (c) 2010 APA, all rights reserved)