Analysis and Diagnostics of Categorical Variables with Multiple Outcomes

<p>Surveys often contain qualitative variables for which respondents may select any number of the outcome categories. For instance, for the question "What type of contraceptive have you used?" with possible responses (oral, condom, lubricated condom, spermicide, and diaphragm), respondents would be instructed to select as many of the J = 5 outcomes as apply. This situation is known as multiple responses and outcomes are referred to as items. This thesis discusses several approaches to analysing such data. For stratified multiple response data, we consider three ways of defining the common odds ratio, a summarising measure for the conditional association between a row variable and the multiple response variable, given a stratification variable. For each stratum, we define the odds ratio in terms of: 1 item and 2 rows, 2 items and 2 rows, and 2 items and 1 row. Then we consider two estimation approaches for the common odds ratio and its (co)variance estimators for these types of odds ratios. The model-based approach treats the J items as a Jdimensional binary response and then uses logit models directly for the marginal distribution of each item by applying the generalised estimating equation (GEE) (Liang and Zeger 1986) method. The non-model-based approach uses Mantel-Haenszel (MH) type estimators. The model-based (or marginal model) approach is still applicable for more than two explanatory variables. Preisser and Qaqish (1996) proposed regression diagnostics for GEE. Another model fitting approach is the homogeneous linear predictor model (HLP) based on maximum likelihood (ML) introduced by Lang (2005). We investigate deletion diagnostics as the Cook distance and DBETA for multiple response data using HLPmodels (Lang 2005), which have not been considered yet, and propose a simple "delete=replace" method as an alternative approach for deletion. Methods are compared with the GEE approach. We also discuss the modelling of a repeated multiple response variable, a categorical variable for which subjects can select any number of categories on repeated occasions. Multiple responses have been considered in the literature by various authors; however, repeated multiple responses have not been considered yet. Approaches include the marginal model approach using the GEE and HLP methods, and generalised linear mixed models (GLMM). For the GEE method, we also consider possible correlation structures and propose a groupwise correlation estimation method yielding more efficient parameter estimates if the correlation structure is indeed different for different groups, which is confirmed by a simulation study. Ordered categorical variables occur in many applications and can be seen as a special case of multiple responses. The proportional odds model, which uses logits of cumulative probabilities, is currently the most popular model. We consider two approaches focusing on the mis-specification of a covariate. The binary approach considers the proportional oddsmodel as J-1 logistic regression models and applies the cumulative residual process introduced by Arbogast and Lin (2005) for logistic regression. The multivariate approach views the proportional odds model as a member of the class of multivariate generalised linear models (MGLM), where the response variable is a vector of indicator responses.</p>

Analysis and Diagnostics of Categorical Variables with Multiple Outcomes

<p>Surveys often contain qualitative variables for which respondents may select any number of the outcome categories. For instance, for the question "What type of contraceptive have you used?" with possible responses (oral, condom, lubricated condom, spermicide, and diaphragm), respondents would be instructed to select as many of the J = 5 outcomes as apply. This situation is known as multiple responses and outcomes are referred to as items. This thesis discusses several approaches to analysing such data. For stratified multiple response data, we consider three ways of defining the common odds ratio, a summarising measure for the conditional association between a row variable and the multiple response variable, given a stratification variable. For each stratum, we define the odds ratio in terms of: 1 item and 2 rows, 2 items and 2 rows, and 2 items and 1 row. Then we consider two estimation approaches for the common odds ratio and its (co)variance estimators for these types of odds ratios. The model-based approach treats the J items as a Jdimensional binary response and then uses logit models directly for the marginal distribution of each item by applying the generalised estimating equation (GEE) (Liang and Zeger 1986) method. The non-model-based approach uses Mantel-Haenszel (MH) type estimators. The model-based (or marginal model) approach is still applicable for more than two explanatory variables. Preisser and Qaqish (1996) proposed regression diagnostics for GEE. Another model fitting approach is the homogeneous linear predictor model (HLP) based on maximum likelihood (ML) introduced by Lang (2005). We investigate deletion diagnostics as the Cook distance and DBETA for multiple response data using HLPmodels (Lang 2005), which have not been considered yet, and propose a simple "delete=replace" method as an alternative approach for deletion. Methods are compared with the GEE approach. We also discuss the modelling of a repeated multiple response variable, a categorical variable for which subjects can select any number of categories on repeated occasions. Multiple responses have been considered in the literature by various authors; however, repeated multiple responses have not been considered yet. Approaches include the marginal model approach using the GEE and HLP methods, and generalised linear mixed models (GLMM). For the GEE method, we also consider possible correlation structures and propose a groupwise correlation estimation method yielding more efficient parameter estimates if the correlation structure is indeed different for different groups, which is confirmed by a simulation study. Ordered categorical variables occur in many applications and can be seen as a special case of multiple responses. The proportional odds model, which uses logits of cumulative probabilities, is currently the most popular model. We consider two approaches focusing on the mis-specification of a covariate. The binary approach considers the proportional oddsmodel as J-1 logistic regression models and applies the cumulative residual process introduced by Arbogast and Lin (2005) for logistic regression. The multivariate approach views the proportional odds model as a member of the class of multivariate generalised linear models (MGLM), where the response variable is a vector of indicator responses.</p>

Statistical Aspects of Community Health and Nutrition

One of the most common problems with the area of health and nutritional research is the limited number of quality books available that can provide research methodology, health indicators and their trend in a single volume. Statistical Aspects of Community Health and Nutrition is a one of the problem-based text book which completely fulfils the gap and stands to our expectations. This book is a single but comprehensive resource on maternal and infant mortality, anemia especially in adolescents and women in reproductive age group and, their causes, prevention, evaluation and validation methods including 30 clusters design, logistic regression and findings of recent relevant studies. Despite above, author also discusses the food insecurity and hunger, tuberculosis, influenza like prevalent diseases, their hotspot and available estimates, techniques for analyzing multiple response data, and small area estimation.

An attempt of process-oriented rainfall-runoff modeling using multiple-response data in an alpine catchment, Loehnersbach, Austria

The development of process-oriented hydrological models, which are able to simulate hydrological processes distributed in space and time, is crucial for optimal management of water resources. The model TACD (tracer aided catchment model, distributed) was modified and applied to the mountainous Loehnersbach catchment (16 km2), Kitzbueheler Alps, Austria, with the aim of simulating the dominant hydrological processes in a distributed way. It can be seen as a further developed, fully distributed version of the HBV-model with a more process-based runoff generation routine, which uses a spatial delineation of hydrological response units (HRUs). Good overall runoff simulations could be obtained for the whole catchment. Additional data, i.e. discharge from sub-catchments, snow height measurements and dissolved silica concentrations, enabled to some extent the evalulation of the simulation of single processes. Certain periods, e.g. short-term runoff fluctuations during snow melt periods, could not be simulated well even when different model modifications were executed. This indicates model shortcomings because of incomplete process understanding and the necessity for further experimental research as well as for new concepts of model structure. In particular, the understanding and mathematical description of subsurface storm flows has to be improved. The impact of different HRU delineations on discharge simulations at the catchment outlet was relatively low, as long as the direct runoff producing units remained constant. However, the impact on runoff predictions at sub-catchment scale was significant. This indicates an ’averaging out’ effect for peculiarities and errors of runoff predictions at larger scales.

Multivariate Analysis of Multiple Response Data

Multiple response questions, also known as a pick any/J format, are frequently encountered in the analysis of survey data. The relationship among the responses is difficult to explore when the number of response options, J, is large. The authors propose a multivariate binomial probit model for analyzing multiple response data and use standard multivariate analysis techniques to conduct exploratory analysis on the latent multivariate normal distribution. A challenge of estimating the probit model is addressing identifying restrictions that lead to the covariance matrix specified with unit-diagonal elements (i.e., a correlation matrix). The authors propose a general approach to handling identifying restrictions and develop specific algorithms for the multivariate binomial probit model. The estimation algorithm is efficient and can easily accommodate many response options that are frequently encountered in the analysis of marketing data. The authors illustrate multivariate analysis of multiple response data in three applications.

Speaking Stata: On Structure and Shape: The Case of Multiple Responses

A frequent problem in data management is that datasets may not arrive in the best structure for many analyses, so that it may be necessary to restructure the data in some way. The particular case of multiple response data is discussed at length, with special attention to different possible structures; the generation of new variables holding the data in different form; valuable inbuilt string and egen functions; using foreach and forvalues to loop over lists; and the use of the reshape command. Tabulations and graphics for such data are also reviewed briefly.