1.3 Structure of the Document

This document is organized according to a logical progression that moves from the conceptual foundations of sampling to more advanced applications of statistical modeling and treatment of nonresponse. This sequence is not arbitrary: each level of knowledge is a necessary prerequisite for understanding the next, allowing the reader to move coherently from basic principles to more sophisticated analytical tools.

First, the foundations of sampling design are addressed. Proper survey analysis necessarily begins with understanding its probability design. Before estimating any parameter, the analyst must become familiar with three constitutive elements: the target population, understood as the set of units about which inferences are to be made; the sampling frame, which corresponds to the operational enumeration of those units; and the sampling units at each stage of the design. These components determine both the validity and the scope of subsequent inferences.

Next, the computational elements that make it possible to materialize these concepts in an applied environment are introduced. The document incorporates variable management and transformation through a programming environment suitable for incorporating the sampling design, which constitutes the central axis of the analytical workflow and ensures that all statistical operations respect that structure.

Once the design has been correctly specified, the document moves on to the estimation of descriptive parameters. This section covers the most commonly used estimators in survey analysis for continuous variables, such as income, expenditure, or assets, including totals, means, and ratios. It also presents their corresponding precision measures, including variances, standard errors, and confidence intervals, adjusted for the complexity of the sampling design.

The document then develops statistical modeling, extending the analysis beyond descriptive statistics toward an analytical and inferential approach. In particular, it addresses linear regression models under complex designs, where the explicit incorporation of sampling weights is fundamental for obtaining design-unbiased estimators. This context highlights the discussion between the design-based approach, which prioritizes statistical properties at the population level, and the model-based approach, which depends on correct functional specification. Consequently, the importance of assessing the sensitivity of results through comparisons between weighted and unweighted estimates is emphasized. In addition, generalized linear models and multilevel models are introduced, broadening the scope of analysis to nonnormal response variables, such as binary variables (logistic regression), counts (Poisson regression), and proportions.

The organization of the chapters follows the conceptual architecture described above, moving from foundations to more complex applications. Chapter 2 presents the basic concepts for household survey analysis, emphasizing that the validity of estimates depends on properly incorporating the sampling design. It explains the central elements of a survey, such as the target population, sampling frame, sampling units, stratification, clustering, and sampling weights. The chapter also introduces the main sampling estimators for totals, means, and other population parameters, and develops the foundations for estimating variance and confidence intervals.

Chapter 3 addresses the rigorous estimation of descriptive parameters for numerical variables under complex designs and develops techniques for estimating totals and means, together with variance estimation through the ultimate cluster method and the construction of confidence intervals with adjusted degrees of freedom. It also presents alternative approaches to variance estimation, such as Taylor linearization, estimating equations, and replication methods, including bootstrap and jackknife. The chapter also covers weighted quantile estimation, inequality analysis using indicators such as the Gini index and the Lorenz curve, estimation in domains and subpopulations, and visualization of results with confidence intervals.

Chapter 4 addresses the analysis of categorical variables under complex designs, including the assessment of associations between categories using methods that properly incorporate the sampling design. It develops techniques for estimating population counts and proportions from weights, together with estimation of their variability through linearization and construction of confidence intervals, including robust approaches for extreme proportions. It also presents weighted contingency tables with their corresponding frequencies and proportions, as well as independence tests that adjust the classical statistic to reflect the design effect. The chapter also covers the estimation and interpretation of association measures such as odds ratios, the analysis of differences in proportions between subpopulations through contrasts, and various visualization strategies, including bar charts with confidence intervals and maps.

Chapter 5 focuses on analyzing relationships between variables and building predictive or explanatory models that are valid under complex designs, when the classical assumptions of independence and identical distribution are not met. It presents the evolution of the problem from early contributions to more recent developments and discusses the implications of working with survey data in the context of regression models, including violations of the assumptions of the classical linear model. It contrasts the design-based approach with the model-based approach. The chapter also addresses hypothesis testing with appropriate adjustments, residual diagnostics, and identification of influential observations.

Chapter 6 extends statistical modeling to variables that do not follow a normal distribution, such as binary, multinomial, and strictly positive variables, in the context of complex sampling designs. To do so, it builds a unified framework based on generalized linear models, incorporating their fundamental components, and discusses inferential duality in finite populations, where the probability measure of the model and that of the sampling design coexist. It also contrasts the classical maximum likelihood approach with maximum pseudo-likelihood, based on weighted estimating equations that incorporate sampling weights, and studies variance estimation through linearization techniques.

Chapter 7 reviews multilevel models, also called hierarchical or mixed-effects models, for analyzing data with a nested structure by simultaneously incorporating individual-level and contextual variables. Through regression examples, with intercepts and slopes that vary by stratum, it shows that ignoring the hierarchical structure can lead to incorrect inferences, whereas modeling it explicitly makes it possible to capture heterogeneity between groups and borrow information across them. The approach is formalized with the null model, which decomposes variance into within-stratum and between-stratum components and allows computation of the intraclass correlation coefficient (ICC), a key indicator for quantifying within-group dependence.

In addition, the first appendix introduces data management in R using the tidyverse environment, with emphasis on the dplyr package. Using the BigCity database, it presents a basic workflow that includes loading libraries, initial inspection of the database, use of the chaining operator %>%, and application of the main dplyr verbs: filter(), select(), arrange(), mutate(), summarise(), and group_by(). The chapter shows how to select records and variables, sort data, create new variables, and produce descriptive summaries, explaining both the logic of the code and the interpretation of its output.

Finally, the second appendix addresses inference in finite populations and the difference between model-based inference and design-based inference. Through simulation examples, it shows that in complex surveys randomness mainly comes from sample selection and that, therefore, estimates must incorporate inclusion probabilities and sampling weights. It presents the maximum likelihood method as a starting point for statistical models under assumptions of independent observations and then presents maximum pseudo-likelihood as an appropriate extension for survey data, where each individual contribution is weighted according to the design.

Readers who go through the chapters in order will have built the capacity to take any Latin American household survey, understand its design, process its data, estimate indicators of interest with the correct statistical precision, model relationships between variables validly under the complex design, and handle nonresponse with appropriate methods. That capacity is, in essence, what rigorous production of social statistics requires.