Review of Interpreting and Visualizing Regression Models Using Stata by Michael N. Mitchell (original) (raw)
Interpretation of Regression Output: Diagnostics, Graphs and the Bottom Line
2002
A standard approach in presenting the results of a statistical analysis of regression data in scientific journals is to focus on the question of statistical significance of regression coefficients. The reporting of p-values in conjunction with a description of the various positive and negative associations between the response and the factors in question ensues. The real question of interest beyond these initial assessments ought to be, "how well does the treatment work?" The point of view taken here will be that this standard presentation, while important, constitutes only a first order approximation to a complete analysis, and that the bottom line ought to involve the quantification of regression effects on the scale of observable quantities. This will mainly be accomplished graphically. It is also emphasized that diagnostic assessment of the compatibility of the data to the model should be based on similar considerations.
Basic Stata Graphics for Economics Students
SSRN Electronic Journal, 2018
This paper provides an introduction to the main types of graph in Stata that economics students might need. It covers univariate discrete and continuous variables, bivariate distributions, some simple time plots and methods of visualising the output from estimating models. It shows a small number of the many options available and includes references to further resources.
2002
A standard approach in presenting the results of a statistical analysis of regression data in scientific journals is to focus on the question of statistical significance of regression coefficients. The reporting of p-values in conjunction with a description of the various positive and negative associations between the response and the factors in question ensues. The real question of interest beyond these initial assessments ought to be, “how well does the treatment work?” The point of view taken here will be that this standard presentation, while important, constitutes only a first order approximation to a complete analysis, and that the bottom line ought to involve the quantification of regression effects on the scale of observable quantities. This will mainly be accomplished graphically. It is also emphasized that diagnostic assessment of the compatibility of the data to the model should be based on similar considerations.
ASA Publications, 2022
Anyone can download it from the links, print it out for personal use, and share it with others, but it is strictly prohibited to use it for any kind of profit-making venture without the written permission of the first author. Its contents may be used and incorporated into other materials with proper acknowledgements and citations. The datasets provided in the links and used in this book are hypothetical and can be used for practice.
This article follows a recommendation from the regression literature to help regression learners become more experienced with residual plots for identifying assumption violations in linear regression. The article goes beyond the usual approach to residual displays in standard regression texts by taking a model-based simulation perspective: simulating the data from a generating model and using them to estimate an analytical model. The analytical model is a first order linear regression model; whereas the generating model violates the assumptions of the analytical model. The residuals from the analytical model are plotted to demonstrate assumption violations to provide experience for regression learners with characterized residual patterns. The article also briefly discusses remedial measures.
REGRESSION ANALYSIS AND RELEVANCE TO RESEARCH IN SOCIAL SCIENCES
Academic Journal of Accounting and Business Management, 2021
The study seeks to review regression analysis and its relevance to research in social sciences, the study relied on a review of various regression analyses being used in social sciences and the significance of regression analysis as a tool in the analysis of data sets. The study adopted a systematic exploratory research design, reviewing related articles, journals, and other prior studies in relation to regression analysis and its relevance in social sciences. After a careful systematic and contextual review, the study revealed that regression analysis is significant in providing a measure of coefficients of the determination which explains the effect of the independent variable (explanatory variable) on the explained variable otherwise known as regressed variables that give the idea of the prediction values of the regression analysis. Regression analysis provides a practical and strong tool for statistical analysis that can enhance investment decisions, business projections in manufacturing, production, stock price movement, sales, and revenue estimations, and generally in making future predictions. This review provides originality in a clear understanding of a comprehensive review of the relevance of regression analysis in social sciences, contributing to knowledge in this regard. The study recommends that researchers should adopt the required pragmatic and methodological steps when using regression analysis, unethical torturing of data should be avoided as this could lead to false results and wrong statistical predictions.
Model fit assessment via marginal model plots
2010
We present a new Stata command, mmp, that generates marginal model plots (Cook and Weisberg, 1997, Journal of the American Statistical Association 92: 490–499) for a regression model. These plots allow for the comparison of the fitted model with a nonparametric or semiparametric model fit. The user may precisely specify how the alternative fit is computed. Demonstrations are given for
Outside and inside the regression ?black box? from exploratory to interior data analysis
Quality & Quantity, 1994
Good data analysis consists of three phases: (f) preliminary analysis, (2) confirmatory analysis (model testing), and (3) interior analysis (model checking). Social scientists doing quantitative research usually concentrate on only one of the three: confirmatory analysis. I argue that there is much to be learned from careful preliminary and interior analyses. I present an extensive example of data analysis for each of the three phases using the same data set in each phase. Rather than surveying all the possible tools available in each phase of data analysis, I concentrate on Exploratory Data Analysis techniques (stem-and-leaf plot, letter-value display, box plot, and power transformations) for the preliminary phase, on OLS for the confirmatory phase, and on residuals, leverage and single-case influence measures for interior analysis.
Biometrical Journal, 2001
We present a graphical measure of assessing the explanatory power of regression models with a binary response. The binary regression quantile plot and an area defined by it are used for the visual comparison and ordering of nested binary response regression models. The plot shows how well various models explain the data. Two data sets are analyzed and the area representing the fit of a model is shown to agree with the usual likelihood ratio test.
Applied Regression Analysis: A Research Tool, Second
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Regression Models 1.1 Introduction
Regression models form the core of the discipline of econometrics. Although econometricians routinely estimate a wide variety of statistical models, using many different types of data, the vast majority of these are either regression models or close relatives of them. In this chapter, we introduce the concept of a regression model, discuss several varieties of them, and introduce the estimation method that is most commonly used with regression models, namely, least squares. This estimation method is derived by using the method of moments, which is a very general principle of estimation that has many applications in econometrics. The most elementary type of regression model is the simple linear regression model, which can be expressed by the following equation: y t = β 1 + β 2 X t + u t. (1.01) The subscript t is used to index the observations of a sample. The total number of observations, also called the sample size, will be denoted by n. Thus, for a sample of size n, the subscript t runs from 1 to n. Each observation comprises an observation on a dependent variable, written as y t for observation t, and an observation on a single explanatory variable, or independent variable, written as X t. The relation (1.01) links the observations on the dependent and the explanatory variables for each observation in terms of two unknown parameters, β 1 and β 2 , and an unobserved error term, u t. Thus, of the five quantities that appear in (1.01), two, y t and X t , are observed, and three, β 1 , β 2 , and u t , are not. Three of them, y t , X t , and u t , are specific to observation t, while the other two, the parameters, are common to all n observations. Here is a simple example of how a regression model like (1.01) could arise in economics. Suppose that the index t is a time index, as the notation suggests. Each value of t could represent a year, for instance. Then y t could be household consumption as measured in year t, and X t could be measured disposable income of households in the same year. In that case, (1.01) would represent what in elementary macroeconomics is called a consumption function.
I n Chapter 2, we learned how to use simple regression analysis to explain a dependent variable, y, as a function of a single independent variable, x. The primary drawback in using simple regression analysis for empirical work is that it is very difficult to draw ceteris paribus conclusions about how x affects y: the key assumption, SLR.4-that all other factors affecting y are uncorrelated with x-is often unrealistic. Multiple regression analysis is more amenable to ceteris paribus analysis because it allows us to explicitly control for many other factors that simultaneously affect the dependent variable. This is important both for testing economic theories and for evaluating policy effects when we must rely on nonexperimental data. Because multiple regression models can accommodate many explanatory variables that may be correlated, we can hope to infer causality in cases where simple regression analysis would be misleading. Naturally, if we add more factors to our model that are useful for explaining y, then more of the variation in y can be explained. Thus, multiple regression analysis can be used to build better models for predicting the dependent variable. An additional advantage of multiple regression analysis is that it can incorporate fairly general functional form relationships. In the simple regression model, only one function of a single explanatory variable can appear in the equation. As we will see, the multiple regression model allows for much more flexibility. Section 3.1 formally introduces the multiple regression model and further discusses the advantages of multiple regression over simple regression. In Section 3.2, we demonstrate how to estimate the parameters in the multiple regression model using the method of ordinary least squares. In Sections 3.3, 3.4, and 3.5, we describe various statistical properties of the OLS estimators, including unbiasedness and efficiency. The multiple regression model is still the most widely used vehicle for empirical analysis in economics and other social sciences. Likewise, the method of ordinary least squares is popularly used for estimating the parameters of the multiple regression model. We begin with some simple examples to show how multiple regression analysis can be used to solve problems that cannot be solved by simple regression. 89782_03_c03_p073-122.qxd 5/26/05 11:46 AM Page 73