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This chapter presents the requirements for conducting a confirmatory factor analysis (CFA). Types of missing data, as well as methods of checking for and addressing missing data, such as imputation, are addressed. Normality is also discussed, including how to assess univariate and multivariate normality as well as estimation methods for non-normal data. Finally, approaches to determining the sample size needed for CFA, such as rules of thumb, the Satorra–Saris method, the MacCallum approach, and the Monte Carlo approach are introduced. Because these issues are quite technical, a brief introduction and suggestions for ways to address each issue, as well as suggested readings for additional information, are provided.

This chapter begins by describing helpful typologies of missing data based on pattern and non-response mechanisms. It then summarizes a collection of commonly used but imperfect methods for dealing with missing data at the analysis stage. Three more rigorous methods, maximum likelihood, multiple imputation, and weighting, are also considered.

This chapter summarizes recent themes and research topics in social statistics, viewed as statistical methods of particular value in substantive research fields such as criminology, demography, economics, education, geography, politics, psychology, public health, social policy, and sociology. Special emphasis is given to multi-level models, small area estimation, models for obtaining measuring instruments, and weighting problems arising in survey data. Particular areas in which further work seems likely to be fruitful are identified by discussing special features connected with incomplete data; policy evaluations; causal inquiries; event history data; aggregate data; macro-level phenomena arising from actions of individuals who influence one another; performance monitoring of public services; and open-source projects for statistical computing.

This chapter assesses the types of questions that have been asked about leaders' traits over time, seeking to better understand the nature of trait structure in the minds of voters. The dimensionality of traits is explored in the existing literature, as well as through the analysis of data from closed-ended traits questions incorporated in thirty-five election studies from seven countries. The chapter analysis suggests the existence of two main dimensions of leaders' characteristics: character and competence. Various methodological issues are explored, including missing data and factor analysis. The two trait dimensions, character and competence, provide a basis for moving forward in the remaining chapters.

Missing data are ubiquitous in ecological and evolutionary data sets as in any other branch of science. The common methods used to deal with missing data are to delete cases containing missing data, and to use the mean to fill in missing values. However, these ‘traditional’ methods will result in biased estimation of parameters and uncertainty, and reduction in statistical power. Now, better missing data procedures such as multiple imputation and data augmentation are readily available and implementable. This chapter introduces the basics of missing data theory—most importantly, the three missing data mechanisms: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR); the chapter also explains relevant concepts of importance such as EM algorithms and MCMC procedures. This chapter enables the application of proper missing data procedures, in particular multiple imputation, using R packages.

Life course functional trajectories are a dynamic way of studying lifetime influences on health and ageing. Gaining a better understanding of trajectories of physical and cognitive capability permits the identification of critical or sensitive periods of development and decline, and of the relative impact of early and later life exposures on these changes. A wide range of analytical tools are available for the description of longitudinal data. The choice of analytical method is based on a match between the method and the question asked, and the decision should be made in the context of study design, the nature of the outcome variable to be modelled, features of the exposure, and the extent of missing observations. This chapter presents a series of statistical models to evaluate specific questions regarding change in single and multiple outcomes, and discusses considerations that affect inferences made when these methods are employed.

This chapter demonstrates how to apply the multilevel model to complex data sets. Section 5.1 begins by illustrating what to do when the number of waves is constant but their spacing is irregular. Section 5.2 illustrates what to do when the number of waves per person differs as well; it also discusses the problem of missing data, the most common source of imbalance in longitudinal work. Section 5.3 demonstrates how to include time-varying predictors in your data analysis. Section 5.4 concludes by discussing why and how to adopt alternative representations for the main effect of TIME.

Because data analyses are only as strong as the data available, Chapter 6 addresses data handling approaches that can be used with primary (i.e., data you collect yourself) or secondary (i.e., data that someone else has collected) survey data, with an emphasis on addressing social justice issues. Chapter 6 begins by addressing preliminary data analyses and “cleaning” that should be completed prior to conducting analyses to answer your research questions. This chapter also briefly discusses issues related to missing data, transformations, computing composite variables, and coding. Although much of the information presented in Chapter 6 is not unique to social justice research, approaching the data handling through a social justice framework may impact some of the data handling decisions that you will make.

It is routine in many fields to collect data having a variety of measurement scales and supports. For example, in biomedical studies for each patient one may collect functional data on a biomarker over time, gene expression values normalized to lie on a hypersphere to remove artifacts, clinical and demographic covariates and a health outcome. A common interest focuses on building predictive models, with parametric assumptions seldom supported by prior knowledge. Hence, it is most appropriate to define a prior with large support allowing the conditional distribution of the response given predictors to be unknown and changing flexibly across the predictor space not just in the mean but also in the variance and shape. Building on earlier work on Dirichlet process mixtures, we describe a simple and general strategy for inducing models for conditional distributions through discrete mixtures of product kernel models for joint distributions of predictors and response variables. Computation is straightforward and the approach can easily accommodate combining of widely disparate data types, including vector data in a Euclidean space, categorical observations, functions, images and manifold data.

Chapter 3 discusses basic concepts in causal inference, beginning with an introduction to potential outcomes and definitions of causal contrasts (or causal estimates of effect), concepts, terms, and notation. Many concepts introduced here will be developed further in subsequent chapters. The author discusses sufficient conditions for estimation of causal effects (which are sometimes called causal identification conditions), causal directed acyclic graphs (sometimes called causal diagrams), and four key types of systematic error (confounding bias, missing data bias, selection bias, and measurement error/information bias). The author also briefly discusses alternative approaches to causal inference.

H‐likelihood refers to a likelihood function of both fixed parameters and random “unobservables,” such as missing data and latent variables. The method then typically proceeds by maximizing over the unobservables via an adjusted profile H‐likelihood, and carries out a Fisher‐information‐like calculation for (predictive) variance estimation. The claimed advantage is its avoidance of all “bad” elements of Bayesian prediction, namely the need for prior specification and posterior integration. This talk attempts to provide an in‐depth look into one of the most intriguing mysteries of modern statistics: why have the proponents of the H‐likelihood method (Lee and Nelder, 1996, 2001, 2005, 2009) been so convinced of its merits when almost everyone else considers it invalid as a general method? The findings are somewhat intriguing themselves. On the one hand, H‐likelihood turns out to be Bartlizable under easily verifiable conditions on the marginal distribution of the unobservables, and such conditions point to a transformation of unobservables that makes it possible to interpret one predictive distribution of the unobservables from three perspectives: Bayesian, fiducial and frequentist. On the other hand, the hope for such a Holy Grail in general is diminished by the fact that the log H‐ likelihood surface cannot generally be summarized quadratically due to the lack of accumulation of information for unobservables, which seems to be the Achilles' Heel of the H‐likelihood method.

This chapter discusses possible solutions for dealing with partial information and missing data from published studies. These solutions can improve the amount of information extracted from individual studies, and increase the representation of data for meta-analysis. It begins with a description of the mechanisms that generate missing information within studies, followed by a discussion of how gaps of information can influence meta-analysis and the way studies are quantitatively reviewed. It then suggests some practical solutions to recovering missing statistics from published studies. These include statistical acrobatics to convert available information (e.g., t-test) into those that are more useful to compute effect sizes, as well as a heuristic approaches that impute (fill gaps) missing information when pooling effect sizes. Finally, the chapter discusses multiple-imputation methods that account for the uncertainty associated with filling gaps of information when performing meta-analysis.

The Fetuses-at-Risk approach can be extended in a number of ways, all related to the use of gestational age as a time axis and cohorts of conceptions, as opposed to cohorts of births, as the appropriate study sample for perinatal epidemiology. This chapter discusses difficulties in interpretation of associations between exposure and measures of mortality based on cohorts of births, and methods that have been developed to summarize fetal and infant mortality into a single measure, post-last menstrual period (post-LMP) mortality, and to model associations between exposures and this outcome using extensions of the Cox proportional hazards model. Similar problems arise in the study of small-for-gestational age, and of weight-for-gestational age in general; these are also discussed in this chapter.

Existing data resources have been used opportunistically to develop thinking about early life beginnings of life long vulnerability, and about long-term exposure to risk. These data resources can provide more insights with new methods of analysis, and possibly pooling and greater harmonization of new data collection. The new, larger, and interdisciplinary life course data resources being developed for epigenetic research will use new methods to measure the impact of current environmental challenges, and should consider in their design the value of data missing by design.

This chapter provides a brief introduction to some of the epidemiologic and statistical methods for, and challenges to, gathering and analyzing the data that underlie the research presented in this volume and in the field of public mental health as a whole. The chapter is not intended as a general introduction to epidemiologic and statistical methods, but focuses more specifically on some of the data and methodological complexities particularly common in public mental health research. Three fundamental types of questions relevant to public mental health are discussed in particular: (1) estimating rates of disorders in a population across people, places, and time; (2) examining risk and protective factors associated with particular disorders; and (3) exploring and understanding the effects of interventions to prevent disorders or to treat them once they emerge.

Model-based inference for distributions and quantiles extends the theory set out in previous chapters to where the target of inference is the finite population distribution function, rather than the finite population total. Inference for quantiles is then carried out by appropriately inverting an efficient predictor of this function. Empirical best predictors under the homogeneous, stratified and linear regression models are described, and their properties discussed. An extension of the empirical best approach to the case where a non-parametric regression fit is more appropriate is developed, as well as an approximation to its prediction variance. An application to imputation for missing data in a wages survey is used to illustrate the comparative performances of the different estimators and the extension to a clustered population model is explored.

This chapter reviews the range of hierarchical modelling. It argues that hierarchical models provide the stochastic framework within which to develop integrative process models. The chapter is organized as follows. Section 3.2 recalls the basics of hierarchical forms, including random effects and missing data. Section 3.3 offers some scope for the introduction of other sorts of latent variables. Section 3.4 considers mixture models while Section 3.5 returns to random effects, primarily in the context of structured dependence. Section 3.6 looks at dynamic models while Section 3.7 considers relatively recent ideas in data fusion. The chapter ends with a brief summary in Section 3.8.

The breeder's equation often fails when applied to natural populations. In large part, this likely occurs because the assumed trait is not the actual target of selection. A within-generation change in the mean of a suggested target trait can arise as a correlated response from selection acting elsewhere. This chapter examines sources of error in the breeder's equation and approaches that attempt to determine if an assumed trait is actually the true target of selection. It also reviews a number of long-term studies from natural populations and examines possible sources for the failure of most of these studies to conform to the expectations of the breeder's equation.

This chapter introduces the mathematics of network statistics, the quantification of errors in network data, and the estimation of network structure in the presence of error. The discussion starts with a summary of the types of error that can occur in network data and the empirical sources of those errors. The remainder of the chapter is given over to a discussion of the theory of network statistics, beginning with a review of the theory for ordinary real-valued (non-network) data, then developing the expectation-maximization (EM) algorithm for estimating network structure and error levels in the presence of error, with example applications. The chapter ends with a discussion of error correction methods such as link prediction and node disambiguation.

In this chapter the authors outline important issues to consider when setting up a survey so that the administration team or a third party vendor is able to conduct meaningful analyses afterward. They discuss decisions surrounding data structure, confidential versus anonymous surveys, and missing data and reporting elements. They also discuss understanding variability, item history, and using norms and benchmark data. The latter part of the chapter focuses on model-building. In summary, it is critical to establish a purpose for a survey and to have a clear strategy for data analysis at the outset to facilitate leaders’ understanding of the data and their ability to act afterward.