Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Now in its second edition, this textbook provides an applied and unified introduction to parametric, nonparametric and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through numerous examples and case studies. The most important definitions and statements are concisely summarized in boxes, and the underlying data sets and code are available online on the book’s dedicated website. Availability of (user-friendly) software has been a major criterion for the methods selected and presented.The chapters address the classical linear model and its extensions, generalized linear models, categorical regression models, mixed models, nonparametric regression, structured additive regression, quantile regression and distributional regression models. Two appendices describe the required matrix algebra, as well as elements of probability calculus and statistical inference.In this substantially revised and updated new edition the overview on regression models has been extended, and now includes the relation between regression models and machine learning, additional details on statistical inference in structured additive regression models have been added and a completely reworked chapter augments the presentation of quantile regression with a comprehensive introduction to distributional regression models. Regularization approaches are now more extensively discussed in most chapters of the book.The book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written at an intermediate mathematical level and assumes only knowledge of basic probability, calculus, matrix algebra and statistics.

Regression analysis. --- Anàlisi de regressió

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book formulates methods for modeling continuous and categorical correlated outcomes that extend the commonly used methods: generalized estimating equations (GEE) and linear mixed modeling. Partially modified GEE adds estimating equations for variance/dispersion parameters to the standard GEE estimating equations for the mean parameters. Fully modified GEE provides alternate estimating equations for mean parameters as well as estimating equations for variance/dispersion parameters. The new estimating equations in these two cases are generated by maximizing a "likelihood" function related to the multivariate normal density function. Partially modified GEE and fully modified GEE use the standard GEE approach to estimate correlation parameters based on the residuals. Extended linear mixed modeling (ELMM) uses the likelihood function to estimate not only mean and variance/dispersion parameters, but also correlation parameters. Formulations are provided for gradient vectors and Hessian matrices, for a multi-step algorithm for solving estimating equations, and model-based and robust empirical tests for assessing theory-based models. Standard GEE, partially modified GEE, fully modified GEE, and ELMM are demonstrated and compared using a variety of regression analyses of different types of correlated outcomes. Example analyses of correlated outcomes include linear regression for continuous outcomes, Poisson regression for count/rate outcomes, logistic regression for dichotomous outcomes, exponential regression for positive-valued continuous outcome, multinomial regression for general polytomous outcomes, ordinal regression for ordinal polytomous outcomes, and discrete regression for discrete numeric outcomes. These analyses also address nonlinearity in predictors based on adaptive search through alternative fractional polynomial models controlled by likelihood cross-validation (LCV) scores. Larger LCV scores indicate better models but not necessarily distinctly better models. LCV ratio tests are used to identify distinctly better models. A SAS macro has been developed for analyzing correlated outcomes using standard GEE, partially modified GEE, fully modified GEE, and ELMM within alternative regression contexts. This macro and code for conducting the analyses addressed in the book are available online via the book’s Springer website. Detailed descriptions of how to use this macro and interpret its output are provided in the book.

Statistics. --- Biometry. --- Statistical Theory and Methods. --- Biostatistics. --- Mathematics. --- Anàlisi de regressió

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Statistical science --- Mathematical statistics --- statistiek --- statistisch onderzoek --- Regression analysis. --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Anàlisi de regressió --- Model de regressió --- Regressió lineal --- Estadística --- Estadística matemàtica --- Correlació múltiple (Estadística) --- Correlació (Estadística) --- Models d'equacions estructurals

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Estadística matemàtica --- Estadística descriptiva --- Inferència estadística --- Matemàtica estadística --- Mètodes estadístics --- Estadística --- Anàlisi d'error (Matemàtica) --- Anàlisi de regressió --- Anàlisi de sèries temporals --- Anàlisi de variància --- Anàlisi multivariable --- Anàlisi seqüencial --- Astronomia estadística --- Correlació (Estadística) --- Dependència (Estadística) --- Estadística no paramètrica --- Estadística robusta --- Física estadística --- Mètode dels moments (Estadística) --- Models lineals (Estadística) --- Models no lineals (Estadística) --- Teoria de l'estimació --- Teoria de la predicció --- Tests d'hipòtesi (Estadística) --- Biometria --- Mostreig (Estadística) --- Mathematical statistics --- Philosophy. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Estadística --- Anàlisi estadística --- Control estadístic --- Informació estadística --- Economia --- Matemàtica --- Allisament (Estadística) --- Anàlisi de regressió --- Anàlisi de variància --- Biometria --- Censos --- Correlació (Estadística) --- Presa de decisions (Estadística) --- Estadística comercial --- Estadística demogràfica --- Estadística econòmica --- Estadística educativa --- Estadística financera --- Estadística industrial --- Estadística matemàtica --- Estadística mèdica --- Mitjana (Estadística) --- Models lineals (Estadística) --- Models no lineals (Estadística) --- Serveis estadístics --- Sondejos d'opinió --- Econometria --- Investigació quantitativa --- Bernoulli numbers. --- Bernoullian numbers --- Numbers, Bernoulli --- Numerical functions