Overview Classes Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)

Size: px
Start display at page:

Download "Overview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)"

Transcription

1 Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) hrs; 5B02 Building and applying loglinear models ( , 9.8) 23-4 Association ( ) hrs: 5A37 Matched pairs (10) 7-5 Repeated measurements (11/12) 14-5 Mixture models (13) 0

2 Logistic Regression Today s topics: 1. Introduction 2. Parameter interpretation 3. Inference 4. Categorical predictors 5. Multiple predictors 6. Software: SPSS 7. Software: lem Sections skipped: 5.5 (except formula 5.20) Logistic regression 5.1

3 Introduction: Logistic Regression The response variable (Y ) is a dichotomous variable. more, continuous or categorical predictor variables. We may have one or For the moment lets consider one predictor variable X. Denote π(x) = P (Y = 1 X = x). The logistic regression model is or equivalently π(x) = logit [π(x)] = log exp(α + βx) 1 + exp(α + βx) π(x) 1 π(x) = α + βx The logit link is equated to the linear predictor. Logistic regression 5.2

4 Interpretation How to interpret β? 1. The sign determines whether the possibility goes up or down with an increase in X. 2. The larger the absolute value of β the steeper the line. When β = 0 the line is flat and X and Y are independent. 3. The relationship between the predictor and the probability follows the logistic curve. Logistic regression 5.3

5 Interpretation P(Y=1 x) x Logistic regression 5.4

6 Interpretation How to interpret β? 1. The odds increase multiplicatively by e β for a unit change in X. 2. e β is an odds ratio. The odds at X = x + 1 divided by the odds at X = x. 3. Use quartiles to get a better understanding. 4. Via linearization argument: The line tangent to the curve has slope βπ(x)[1 π(x)]. This is approximately the increase in probability with an increase in predictor value of From this, it follows that near x where π(x) =.5, (i.e., x = α/β) 1/β approximates the distance between x-values that correspond to π(x) =.25 or π(x) =.75 and π(x) =.5. Logistic regression 5.5

7 Inference Significance tests usually test H 0 : β = 0. Possible tests (see class 1): 1. Wald statistic: z = β/se. z 2 χ 2 with df=1. 2. Likelihood ratio statistic; Uses the difference of twice the maximized loglikelihood at ˆβ and β = 0. Also chi-square distributed with df=1. The likelihood ratio statistic is preferred over the Wald statistic. It uses more information and has more power. More information is usually provided by confidence intervals for β. These are arrived through inverse reasoning. Logistic regression 5.6

8 Inference Often we also like a confidence interval for the predicted probabilities (ˆπ(x)). For a fixed value x = x 0, logit[ˆπ(x 0 )] = ˆα + ˆβx 0 has a large-sample standard error (SE) given by the square root of var(ˆα + ˆβx 0 ) = var(ˆα) + x 2 0 var(ˆβ) + 2x 0 cov(ˆα, ˆβ) The variances and covariances of the regression weights can be obtained from formula (5.20). A 95%-confidence interval for the logit is obtained by adding and subtracting 1.96SE from the estimated logit. From this confidence interval we can obtain a confidence interval for the probabilities by π(x 0 ) = exp(logit) 1 + exp(logit) Logistic regression 5.7

9 Inference: Goodness-of-fit stats In practice there is no guarantee that the model fits the data well. But if all more complex models do not increase the fit then this is some evidence that the chosen model is reasonable. Detecting lack of fit by searching any way that the model fails. Therefore, X 2 and G 2 statistics are used. Data must be grouped: Categorize continuous variables. An example is the Hosmer and Lemeshow statistic: Partition the data in g (approximately) equal groups based on predicted probabilities. Then form a contingency table of the groups against the two response categories. Compare fitted and observed frequencies. Such tests indicate lack of fit but no insight about its nature. Logistic regression 5.8

10 Categorical predictors Categorical variables are often named factors. log ( πi 1 π i ) = α + β i One must constrain one of the β i s, for example β 1 = 0 or i β i = 0. This is like the ANOVA model Logistic regression 5.9

11 Categorical predictors The same model can be made using dummy variables. A factor with I levels needs I 1 dummy variables. Like in multiple regression with dummy variables. Example of dummy-variables for three-category Effect Dummy x 1 x 2 x 1 x log ( πi 1 π i ) = α + β 1 x 1 + β 2 x 2... In effect coding the β i represents deviance from a mean. In dummy coding the β i denote deviance from the baseline group for which we set β i = 0. Logistic regression 5.10

12 Categorical predictors Effect coding corresponds with the constraint i β i = 0 in the ANOVA set-up whereas Dummy-coding corresponds with β I = 0. Depending on the dummies chosen, the interpretation of β i changes. However, model fit does not change. Whatever constraint is chosen ˆα + ˆβ i does not change and so the probabilities remain the same. The differences ˆβ a ˆβ b for any pair (a, b) represent estimated log-odds ratios Logistic regression 5.11

13 Ordered Categorical predictors If there are ordered categorical predictors for which we can find sensible scores (x 1, x 2,..., x I ) these scores might be used and we act as if the predictor is of interval level. An advantage is that we have increased power if most of the relationship between predictor and logit is linear. We only use one degree of freedom. Disadvantage: When the relationship between predictor and the logit is nonlinear we loose valuable information. Logistic regression 5.12

14 Multiple predictors Like in ordinary regression, logistic regression extends to cases with multiple predictors. Let π(x) = P (Y = 1 X 1 = x 1, X 2 = x 2,..., X p = x p ), then π(x) = exp(α + β 1x 1 + β 2 x β p x p ) 1 exp(α + β 1 x 1 + β 2 x β p x p ) The parameters β i refers to the effect of x i on the log odds that Y = 1, controlling for the other x j (i.e. keeping the other x j fixed). The predictor variables can, of course, be categorical (dummy) or continuous. When all predictors are categorical the data can be represented in a contingency table format. (The data has grouped format). With factors the ANOVA-model is written as ) log ( πi 1 π i = α + β X i + β Z k Logistic regression 5.13

15 Multiple predictors Are predictors important? 1. Use the Wald statistic (ˆβ 2 /SE 2 ). 2. Use the likelihood ratio test. Compare two nested models, M 0 and M 1 with maximized log likelihood values L 0 and L 1, respectively. Denote assuming that model M 1 holds. G 2 (M 0 M 1 ) = 2(L 0 L 1 ), G 2 (M 0 M 1 ) = 2(L 0 L 1 ) has a chi-squared statistic with df the difference in number of (independent!) parameters of the two models. Logistic regression 5.14

16 SPSS SPSS has under Analyze > Regression > Binary Logistic.. a logistic regression program. Contains many statistics, such as 1. many residuals 2. the Hosmer and Lemeshow statistic 3. influence diagnostics (to be discussed next week) 4. etc Logistic regression 5.15

17 lem Program for categorical data analysis (free!) Can be found at: This program is especially useful for the analysis of contingency tables but it can do much more (See examples ). Logistic regression 5.16

STATISTICA Formula Guide: Logistic Regression. Table of Contents

STATISTICA Formula Guide: Logistic Regression. Table of Contents : Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary

More information

11. Analysis of Case-control Studies Logistic Regression

11. Analysis of Case-control Studies Logistic Regression Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

More information

Ordinal Regression. Chapter

Ordinal Regression. Chapter Ordinal Regression Chapter 4 Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe

More information

VI. Introduction to Logistic Regression

VI. Introduction to Logistic Regression VI. Introduction to Logistic Regression We turn our attention now to the topic of modeling a categorical outcome as a function of (possibly) several factors. The framework of generalized linear models

More information

LOGISTIC REGRESSION ANALYSIS

LOGISTIC REGRESSION ANALYSIS LOGISTIC REGRESSION ANALYSIS C. Mitchell Dayton Department of Measurement, Statistics & Evaluation Room 1230D Benjamin Building University of Maryland September 1992 1. Introduction and Model Logistic

More information

13. Poisson Regression Analysis

13. Poisson Regression Analysis 136 Poisson Regression Analysis 13. Poisson Regression Analysis We have so far considered situations where the outcome variable is numeric and Normally distributed, or binary. In clinical work one often

More information

Multivariate Logistic Regression

Multivariate Logistic Regression 1 Multivariate Logistic Regression As in univariate logistic regression, let π(x) represent the probability of an event that depends on p covariates or independent variables. Then, using an inv.logit formulation

More information

Logit Models for Binary Data

Logit Models for Binary Data Chapter 3 Logit Models for Binary Data We now turn our attention to regression models for dichotomous data, including logistic regression and probit analysis. These models are appropriate when the response

More information

The Probit Link Function in Generalized Linear Models for Data Mining Applications

The Probit Link Function in Generalized Linear Models for Data Mining Applications Journal of Modern Applied Statistical Methods Copyright 2013 JMASM, Inc. May 2013, Vol. 12, No. 1, 164-169 1538 9472/13/$95.00 The Probit Link Function in Generalized Linear Models for Data Mining Applications

More information

SAS Software to Fit the Generalized Linear Model

SAS Software to Fit the Generalized Linear Model SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling

More information

Generalized Linear Models

Generalized Linear Models Generalized Linear Models We have previously worked with regression models where the response variable is quantitative and normally distributed. Now we turn our attention to two types of models where the

More information

Linear Regression in SPSS

Linear Regression in SPSS Linear Regression in SPSS Data: mangunkill.sav Goals: Examine relation between number of handguns registered (nhandgun) and number of man killed (mankill) checking Predict number of man killed using number

More information

Multinomial and Ordinal Logistic Regression

Multinomial and Ordinal Logistic Regression Multinomial and Ordinal Logistic Regression ME104: Linear Regression Analysis Kenneth Benoit August 22, 2012 Regression with categorical dependent variables When the dependent variable is categorical,

More information

Logistic Regression. http://faculty.chass.ncsu.edu/garson/pa765/logistic.htm#sigtests

Logistic Regression. http://faculty.chass.ncsu.edu/garson/pa765/logistic.htm#sigtests Logistic Regression http://faculty.chass.ncsu.edu/garson/pa765/logistic.htm#sigtests Overview Binary (or binomial) logistic regression is a form of regression which is used when the dependent is a dichotomy

More information

Simple Linear Regression Inference

Simple Linear Regression Inference Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

More information

Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.)

Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Logistic regression generalizes methods for 2-way tables Adds capability studying several predictors, but Limited to

More information

Logistic Regression (1/24/13)

Logistic Regression (1/24/13) STA63/CBB540: Statistical methods in computational biology Logistic Regression (/24/3) Lecturer: Barbara Engelhardt Scribe: Dinesh Manandhar Introduction Logistic regression is model for regression used

More information

Lecture 13: Introduction to generalized linear models

Lecture 13: Introduction to generalized linear models Lecture 13: Introduction to generalized linear models 21 November 2007 1 Introduction Recall that we ve looked at linear models, which specify a conditional probability density P(Y X) of the form Y = α

More information

5. Ordinal regression: cumulative categories proportional odds. 6. Ordinal regression: comparison to single reference generalized logits

5. Ordinal regression: cumulative categories proportional odds. 6. Ordinal regression: comparison to single reference generalized logits Lecture 23 1. Logistic regression with binary response 2. Proc Logistic and its surprises 3. quadratic model 4. Hosmer-Lemeshow test for lack of fit 5. Ordinal regression: cumulative categories proportional

More information

Weight of Evidence Module

Weight of Evidence Module Formula Guide The purpose of the Weight of Evidence (WoE) module is to provide flexible tools to recode the values in continuous and categorical predictor variables into discrete categories automatically,

More information

Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus

Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus Tihomir Asparouhov and Bengt Muthén Mplus Web Notes: No. 15 Version 8, August 5, 2014 1 Abstract This paper discusses alternatives

More information

Poisson Regression or Regression of Counts (& Rates)

Poisson Regression or Regression of Counts (& Rates) Poisson Regression or Regression of (& Rates) Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Generalized Linear Models Slide 1 of 51 Outline Outline

More information

Module 4 - Multiple Logistic Regression

Module 4 - Multiple Logistic Regression Module 4 - Multiple Logistic Regression Objectives Understand the principles and theory underlying logistic regression Understand proportions, probabilities, odds, odds ratios, logits and exponents Be

More information

Regression III: Advanced Methods

Regression III: Advanced Methods Lecture 16: Generalized Additive Models Regression III: Advanced Methods Bill Jacoby Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Goals of the Lecture Introduce Additive Models

More information

Poisson Models for Count Data

Poisson Models for Count Data Chapter 4 Poisson Models for Count Data In this chapter we study log-linear models for count data under the assumption of a Poisson error structure. These models have many applications, not only to the

More information

Lecture 18: Logistic Regression Continued

Lecture 18: Logistic Regression Continued Lecture 18: Logistic Regression Continued Dipankar Bandyopadhyay, Ph.D. BMTRY 711: Analysis of Categorical Data Spring 2011 Division of Biostatistics and Epidemiology Medical University of South Carolina

More information

Developing Risk Adjustment Techniques Using the SAS@ System for Assessing Health Care Quality in the lmsystem@

Developing Risk Adjustment Techniques Using the SAS@ System for Assessing Health Care Quality in the lmsystem@ Developing Risk Adjustment Techniques Using the SAS@ System for Assessing Health Care Quality in the lmsystem@ Yanchun Xu, Andrius Kubilius Joint Commission on Accreditation of Healthcare Organizations,

More information

Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

More information

" Y. Notation and Equations for Regression Lecture 11/4. Notation:

 Y. Notation and Equations for Regression Lecture 11/4. Notation: Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

More information

Yiming Peng, Department of Statistics. February 12, 2013

Yiming Peng, Department of Statistics. February 12, 2013 Regression Analysis Using JMP Yiming Peng, Department of Statistics February 12, 2013 2 Presentation and Data http://www.lisa.stat.vt.edu Short Courses Regression Analysis Using JMP Download Data to Desktop

More information

Logistic regression diagnostics

Logistic regression diagnostics Logistic regression diagnostics Biometry 755 Spring 2009 Logistic regression diagnostics p. 1/28 Assessing model fit A good model is one that fits the data well, in the sense that the values predicted

More information

INTRODUCTORY STATISTICS

INTRODUCTORY STATISTICS INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore

More information

Lecture 19: Conditional Logistic Regression

Lecture 19: Conditional Logistic Regression Lecture 19: Conditional Logistic Regression Dipankar Bandyopadhyay, Ph.D. BMTRY 711: Analysis of Categorical Data Spring 2011 Division of Biostatistics and Epidemiology Medical University of South Carolina

More information

HLM software has been one of the leading statistical packages for hierarchical

HLM software has been one of the leading statistical packages for hierarchical Introductory Guide to HLM With HLM 7 Software 3 G. David Garson HLM software has been one of the leading statistical packages for hierarchical linear modeling due to the pioneering work of Stephen Raudenbush

More information

Binary Logistic Regression

Binary Logistic Regression Binary Logistic Regression Main Effects Model Logistic regression will accept quantitative, binary or categorical predictors and will code the latter two in various ways. Here s a simple model including

More information

Assumptions. Assumptions of linear models. Boxplot. Data exploration. Apply to response variable. Apply to error terms from linear model

Assumptions. Assumptions of linear models. Boxplot. Data exploration. Apply to response variable. Apply to error terms from linear model Assumptions Assumptions of linear models Apply to response variable within each group if predictor categorical Apply to error terms from linear model check by analysing residuals Normality Homogeneity

More information

Logit and Probit. Brad Jones 1. April 21, 2009. University of California, Davis. Bradford S. Jones, UC-Davis, Dept. of Political Science

Logit and Probit. Brad Jones 1. April 21, 2009. University of California, Davis. Bradford S. Jones, UC-Davis, Dept. of Political Science Logit and Probit Brad 1 1 Department of Political Science University of California, Davis April 21, 2009 Logit, redux Logit resolves the functional form problem (in terms of the response function in the

More information

I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Beckman HLM Reading Group: Questions, Answers and Examples Carolyn J. Anderson Department of Educational Psychology I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Linear Algebra Slide 1 of

More information

Using Stata 11 & higher for Logistic Regression Richard Williams, University of Notre Dame, Last revised March 28, 2015

Using Stata 11 & higher for Logistic Regression Richard Williams, University of Notre Dame,  Last revised March 28, 2015 Using Stata 11 & higher for Logistic Regression Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised March 28, 2015 NOTE: The routines spost13, lrdrop1, and extremes are

More information

III. INTRODUCTION TO LOGISTIC REGRESSION. a) Example: APACHE II Score and Mortality in Sepsis

III. INTRODUCTION TO LOGISTIC REGRESSION. a) Example: APACHE II Score and Mortality in Sepsis III. INTRODUCTION TO LOGISTIC REGRESSION 1. Simple Logistic Regression a) Example: APACHE II Score and Mortality in Sepsis The following figure shows 30 day mortality in a sample of septic patients as

More information

Statistics in Retail Finance. Chapter 6: Behavioural models

Statistics in Retail Finance. Chapter 6: Behavioural models Statistics in Retail Finance 1 Overview > So far we have focussed mainly on application scorecards. In this chapter we shall look at behavioural models. We shall cover the following topics:- Behavioural

More information

LOGIT AND PROBIT ANALYSIS

LOGIT AND PROBIT ANALYSIS LOGIT AND PROBIT ANALYSIS A.K. Vasisht I.A.S.R.I., Library Avenue, New Delhi 110 012 amitvasisht@iasri.res.in In dummy regression variable models, it is assumed implicitly that the dependent variable Y

More information

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm

More information

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not. Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C

More information

Logistic regression modeling the probability of success

Logistic regression modeling the probability of success Logistic regression modeling the probability of success Regression models are usually thought of as only being appropriate for target variables that are continuous Is there any situation where we might

More information

Logistic Regression. Jia Li. Department of Statistics The Pennsylvania State University. Logistic Regression

Logistic Regression. Jia Li. Department of Statistics The Pennsylvania State University. Logistic Regression Logistic Regression Department of Statistics The Pennsylvania State University Email: jiali@stat.psu.edu Logistic Regression Preserve linear classification boundaries. By the Bayes rule: Ĝ(x) = arg max

More information

Statistics in Retail Finance. Chapter 2: Statistical models of default

Statistics in Retail Finance. Chapter 2: Statistical models of default Statistics in Retail Finance 1 Overview > We consider how to build statistical models of default, or delinquency, and how such models are traditionally used for credit application scoring and decision

More information

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate

More information

Regression Analysis: Basic Concepts

Regression Analysis: Basic Concepts The simple linear model Regression Analysis: Basic Concepts Allin Cottrell Represents the dependent variable, y i, as a linear function of one independent variable, x i, subject to a random disturbance

More information

Sun Li Centre for Academic Computing lsun@smu.edu.sg

Sun Li Centre for Academic Computing lsun@smu.edu.sg Sun Li Centre for Academic Computing lsun@smu.edu.sg Elementary Data Analysis Group Comparison & One-way ANOVA Non-parametric Tests Correlations General Linear Regression Logistic Models Binary Logistic

More information

Examples of Using R for Modeling Ordinal Data

Examples of Using R for Modeling Ordinal Data Examples of Using R for Modeling Ordinal Data Alan Agresti Department of Statistics, University of Florida Supplement for the book Analysis of Ordinal Categorical Data, 2nd ed., 2010 (Wiley), abbreviated

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

When to Use a Particular Statistical Test

When to Use a Particular Statistical Test When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21 - mode = 21 Median the center value the

More information

CREDIT SCORING MODEL APPLICATIONS:

CREDIT SCORING MODEL APPLICATIONS: Örebro University Örebro University School of Business Master in Applied Statistics Thomas Laitila Sune Karlsson May, 2014 CREDIT SCORING MODEL APPLICATIONS: TESTING MULTINOMIAL TARGETS Gabriela De Rossi

More information

Elements of statistics (MATH0487-1)

Elements of statistics (MATH0487-1) Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -

More information

Title. Syntax. Menu. Description. stata.com. lrtest Likelihood-ratio test after estimation. modelspec2. lrtest modelspec 1.

Title. Syntax. Menu. Description. stata.com. lrtest Likelihood-ratio test after estimation. modelspec2. lrtest modelspec 1. Title stata.com lrtest Likelihood-ratio test after estimation Syntax Menu Description Options Remarks and examples Stored results Methods and formulas References Also see Syntax lrtest modelspec 1 [ modelspec2

More information

MORE ON LOGISTIC REGRESSION

MORE ON LOGISTIC REGRESSION DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 816 MORE ON LOGISTIC REGRESSION I. AGENDA: A. Logistic regression 1. Multiple independent variables 2. Example: The Bell Curve 3. Evaluation

More information

Multiple logistic regression analysis of cigarette use among high school students

Multiple logistic regression analysis of cigarette use among high school students Multiple logistic regression analysis of cigarette use among high school students ABSTRACT Joseph Adwere-Boamah Alliant International University A binary logistic regression analysis was performed to predict

More information

Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences

Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences Third Edition Jacob Cohen (deceased) New York University Patricia Cohen New York State Psychiatric Institute and Columbia University

More information

Lecture #2 Overview. Basic IRT Concepts, Models, and Assumptions. Lecture #2 ICPSR Item Response Theory Workshop

Lecture #2 Overview. Basic IRT Concepts, Models, and Assumptions. Lecture #2 ICPSR Item Response Theory Workshop Basic IRT Concepts, Models, and Assumptions Lecture #2 ICPSR Item Response Theory Workshop Lecture #2: 1of 64 Lecture #2 Overview Background of IRT and how it differs from CFA Creating a scale An introduction

More information

Response variables assume only two values, say Y j = 1 or = 0, called success and failure (spam detection, credit scoring, contracting.

Response variables assume only two values, say Y j = 1 or = 0, called success and failure (spam detection, credit scoring, contracting. Prof. Dr. J. Franke All of Statistics 1.52 Binary response variables - logistic regression Response variables assume only two values, say Y j = 1 or = 0, called success and failure (spam detection, credit

More information

Generalized Linear Models. Today: definition of GLM, maximum likelihood estimation. Involves choice of a link function (systematic component)

Generalized Linear Models. Today: definition of GLM, maximum likelihood estimation. Involves choice of a link function (systematic component) Generalized Linear Models Last time: definition of exponential family, derivation of mean and variance (memorize) Today: definition of GLM, maximum likelihood estimation Include predictors x i through

More information

General Regression Formulae ) (N-2) (1 - r 2 YX

General Regression Formulae ) (N-2) (1 - r 2 YX General Regression Formulae Single Predictor Standardized Parameter Model: Z Yi = β Z Xi + ε i Single Predictor Standardized Statistical Model: Z Yi = β Z Xi Estimate of Beta (Beta-hat: β = r YX (1 Standard

More information

The Proportional Odds Model for Assessing Rater Agreement with Multiple Modalities

The Proportional Odds Model for Assessing Rater Agreement with Multiple Modalities The Proportional Odds Model for Assessing Rater Agreement with Multiple Modalities Elizabeth Garrett-Mayer, PhD Assistant Professor Sidney Kimmel Comprehensive Cancer Center Johns Hopkins University 1

More information

Use of deviance statistics for comparing models

Use of deviance statistics for comparing models A likelihood-ratio test can be used under full ML. The use of such a test is a quite general principle for statistical testing. In hierarchical linear models, the deviance test is mostly used for multiparameter

More information

Statistical Machine Learning

Statistical Machine Learning Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes

More information

Interactions involving Categorical Predictors

Interactions involving Categorical Predictors Interactions involving Categorical Predictors Today s Class: To CLASS or not to CLASS: Manual vs. program-created differences among groups Interactions of continuous and categorical predictors Interactions

More information

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

More information

Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

More information

Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 13 Introduction to Linear Regression and Correlation Analysis Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

More information

Directions for using SPSS

Directions for using SPSS Directions for using SPSS Table of Contents Connecting and Working with Files 1. Accessing SPSS... 2 2. Transferring Files to N:\drive or your computer... 3 3. Importing Data from Another File Format...

More information

Two Correlated Proportions (McNemar Test)

Two Correlated Proportions (McNemar Test) Chapter 50 Two Correlated Proportions (Mcemar Test) Introduction This procedure computes confidence intervals and hypothesis tests for the comparison of the marginal frequencies of two factors (each with

More information

Statistical Models in R

Statistical Models in R Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova

More information

Local classification and local likelihoods

Local classification and local likelihoods Local classification and local likelihoods November 18 k-nearest neighbors The idea of local regression can be extended to classification as well The simplest way of doing so is called nearest neighbor

More information

Models for Count Data With Overdispersion

Models for Count Data With Overdispersion Models for Count Data With Overdispersion Germán Rodríguez November 6, 2013 Abstract This addendum to the WWS 509 notes covers extra-poisson variation and the negative binomial model, with brief appearances

More information

Statistics 305: Introduction to Biostatistical Methods for Health Sciences

Statistics 305: Introduction to Biostatistical Methods for Health Sciences Statistics 305: Introduction to Biostatistical Methods for Health Sciences Modelling the Log Odds Logistic Regression (Chap 20) Instructor: Liangliang Wang Statistics and Actuarial Science, Simon Fraser

More information

Linear Models for Continuous Data

Linear Models for Continuous Data Chapter 2 Linear Models for Continuous Data The starting point in our exploration of statistical models in social research will be the classical linear model. Stops along the way include multiple linear

More information

Study Guide for the Final Exam

Study Guide for the Final Exam Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

More information

Multinomial Logistic Regression

Multinomial Logistic Regression Multinomial Logistic Regression Dr. Jon Starkweather and Dr. Amanda Kay Moske Multinomial logistic regression is used to predict categorical placement in or the probability of category membership on a

More information

Linda K. Muthén Bengt Muthén. Copyright 2008 Muthén & Muthén www.statmodel.com. Table Of Contents

Linda K. Muthén Bengt Muthén. Copyright 2008 Muthén & Muthén www.statmodel.com. Table Of Contents Mplus Short Courses Topic 2 Regression Analysis, Eploratory Factor Analysis, Confirmatory Factor Analysis, And Structural Equation Modeling For Categorical, Censored, And Count Outcomes Linda K. Muthén

More information

Variance of OLS Estimators and Hypothesis Testing. Randomness in the model. GM assumptions. Notes. Notes. Notes. Charlie Gibbons ARE 212.

Variance of OLS Estimators and Hypothesis Testing. Randomness in the model. GM assumptions. Notes. Notes. Notes. Charlie Gibbons ARE 212. Variance of OLS Estimators and Hypothesis Testing Charlie Gibbons ARE 212 Spring 2011 Randomness in the model Considering the model what is random? Y = X β + ɛ, β is a parameter and not random, X may be

More information

Supplementary PROCESS Documentation

Supplementary PROCESS Documentation Supplementary PROCESS Documentation This document is an addendum to Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis that describes options and output added to PROCESS

More information

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association

More information

Chapter 3 Quantitative Demand Analysis

Chapter 3 Quantitative Demand Analysis Managerial Economics & Business Strategy Chapter 3 uantitative Demand Analysis McGraw-Hill/Irwin Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. Overview I. The Elasticity Concept

More information

Data Mining: An Overview of Methods and Technologies for Increasing Profits in Direct Marketing. C. Olivia Rud, VP, Fleet Bank

Data Mining: An Overview of Methods and Technologies for Increasing Profits in Direct Marketing. C. Olivia Rud, VP, Fleet Bank Data Mining: An Overview of Methods and Technologies for Increasing Profits in Direct Marketing C. Olivia Rud, VP, Fleet Bank ABSTRACT Data Mining is a new term for the common practice of searching through

More information

Structural Equation Models for Comparing Dependent Means and Proportions. Jason T. Newsom

Structural Equation Models for Comparing Dependent Means and Proportions. Jason T. Newsom Structural Equation Models for Comparing Dependent Means and Proportions Jason T. Newsom How to Do a Paired t-test with Structural Equation Modeling Jason T. Newsom Overview Rationale Structural equation

More information

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall

More information

Prediction and Confidence Intervals in Regression

Prediction and Confidence Intervals in Regression Fall Semester, 2001 Statistics 621 Lecture 3 Robert Stine 1 Prediction and Confidence Intervals in Regression Preliminaries Teaching assistants See them in Room 3009 SH-DH. Hours are detailed in the syllabus.

More information

Survival Analysis Using SPSS. By Hui Bian Office for Faculty Excellence

Survival Analysis Using SPSS. By Hui Bian Office for Faculty Excellence Survival Analysis Using SPSS By Hui Bian Office for Faculty Excellence Survival analysis What is survival analysis Event history analysis Time series analysis When use survival analysis Research interest

More information

CHAPTER 12 EXAMPLES: MONTE CARLO SIMULATION STUDIES

CHAPTER 12 EXAMPLES: MONTE CARLO SIMULATION STUDIES Examples: Monte Carlo Simulation Studies CHAPTER 12 EXAMPLES: MONTE CARLO SIMULATION STUDIES Monte Carlo simulation studies are often used for methodological investigations of the performance of statistical

More information

SUGI 29 Statistics and Data Analysis

SUGI 29 Statistics and Data Analysis Paper 194-29 Head of the CLASS: Impress your colleagues with a superior understanding of the CLASS statement in PROC LOGISTIC Michelle L. Pritchard and David J. Pasta Ovation Research Group, San Francisco,

More information

Using An Ordered Logistic Regression Model with SAS Vartanian: SW 541

Using An Ordered Logistic Regression Model with SAS Vartanian: SW 541 Using An Ordered Logistic Regression Model with SAS Vartanian: SW 541 libname in1 >c:\=; Data first; Set in1.extract; A=1; PROC LOGIST OUTEST=DD MAXITER=100 ORDER=DATA; OUTPUT OUT=CC XBETA=XB P=PROB; MODEL

More information

Regression Modeling Strategies

Regression Modeling Strategies Frank E. Harrell, Jr. Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival Analysis With 141 Figures Springer Contents Preface Typographical Conventions

More information

Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests. The Applied Research Center Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

More information

Modeling Lifetime Value in the Insurance Industry

Modeling Lifetime Value in the Insurance Industry Modeling Lifetime Value in the Insurance Industry C. Olivia Parr Rud, Executive Vice President, Data Square, LLC ABSTRACT Acquisition modeling for direct mail insurance has the unique challenge of targeting

More information

The aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree

The aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree PS 511: Advanced Statistics for Psychological and Behavioral Research 1 Both examine linear (straight line) relationships Correlation works with a pair of scores One score on each of two variables ( and

More information

Logistic Regression 1. y log( ) logit( y) 1 y = = +

Logistic Regression 1. y log( ) logit( y) 1 y = = + Written by: Robin Beaumont e-mail: robin@organplayers.co.uk Date Thursday, 05 July 2012 Version: 3 Logistic Regression model Can be converted to a probability dependent variable = outcome/event log odds

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96 1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

More information

Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS

Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple

More information

Logistic Regression (a type of Generalized Linear Model)

Logistic Regression (a type of Generalized Linear Model) Logistic Regression (a type of Generalized Linear Model) 1/36 Today Review of GLMs Logistic Regression 2/36 How do we find patterns in data? We begin with a model of how the world works We use our knowledge

More information