VI. Introduction to Logistic Regression


 Naomi Morgan
 2 years ago
 Views:
Transcription
1 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 unifies a family of regression models that includes (but is not limited to) logistic, Poisson, and linear regression.
2 Linear Regression: Modeling the Mean Recall that linear regression involves modeling the mean of some outcome variable as a function of one or more explanatory variables. That is, we have a sample Y 1,, Y n of independent measures, where the i th subject in our sample has p explanatory variables x i1, x i2,, x ip, and E(Y i ) = μ i. The linear regression model specifies that Y i = β 0 + β 1 x i1 + β 2 x i2 + + β p x ip + ε i, where ε i ~ N(0, σ 2 ), for i = 1,,n. Then E(Y i x i1, x i2,, x ip ) = β 0 + β 1 x i1 + + β p x ip, and Var(Y i ) = σ 2. This model assumes that the mean of the outcome variable changes linearly with respect to the explanatory variables.
3 The Three Components of a Generalized Linear Model Whereas with linear regression, we model the mean of the outcome variable directly, a generalized linear model is constructed to model the effects of the covariates on a function of the mean. There are hence three parts or components that comprise a generalized linear model: 1. The random component, which specifies the distribution of the outcome variable. 2. The systematic component, which represents a function of the covariates that will link to the outcome variable. 3. The link function, which determines how the mean of the outcome variable relates to the covariates.
4 Generalized Linear Models for Binary Data We have a sample Y 1,, Y n of independent binary outcome measurements. The i th subject in our sample has p explanatory variables x i1, x i2,, x ip. Suppose that P(Y i = 1) = π i and P(Y i = 0) = 1 π i. Hence, E(Y i ) = π i. The random component in this case is clearly binomial. For the purpose of this class, we will always assume that the systematic component is simply a linear combination of the covariates, or β 0 + β 1 x i1 + + β p x ip. The remaining question is: how do we model π i as a function of the covariates (i.e., what is the link function)?
5 Link Functions for the Binomial Distribution Suppose that we assume that E(Y i ) = π i = β 0 + β 1 x i1 + + β p x ip. We call this the identity link. Does this model have any practical shortcomings? Since the systematic component can take on any value, we often prefer using a link that t will constrain π i to the interval lbetween 0 and 1. The socalled logistic (also called the logit or logodds) link g(π i ) = log[π i /(1 π i )] accomplishes this. There are other links (e.g., the probit), but we will focus mainly on the logit.
6 Example VI.A The Cache County Memory Study (CCMS) has followed approximately 5100 elderly l men and women continually since The project s focus has been to better understand genetic and environmental modifiers of dementia risk particularly Alzheimer s disease and cognitive health. The ε4 allele of the APOE gene is a reported risk factor for AD. The data in the following table summarize findings (thus far) from the CCMS relative to APOE and AD. AD No AD Total 1 ε4 Allele No ε Total
7 Example VI.A Consider a generalized linear model in this case. Note that these data can be viewed as a sample of outcome measures Y 1,,YY 4962, where Y i = 1 if the i th individual was diagnosed with AD, and Y i = 0 otherwise. Moreover, we have a single covariate X i, which is 1 if the i th individual has at least one copy of the APOE ε4 allele, and 0 otherwise. The model looks something like this: logit(π i ) = log[π i /(1 π i )] = β 0 + β 1 X i
8 Example VI.A (cont d) First, how do we interpret the coefficients of this model? What is logit(π i X i = 1)? What is logit(π i X i = 0)? What is the log odds ratio with respect to AD risk, comparing those with at least one ε4 to those with no ε4? The regression coefficient of a binary covariate in a logistic regression model represents the log odds ratio comparing the group identified as 1 to the group identified as 0. More generally, the coefficient of any arbitrary covariate in a logistic regression model represents the log odds ratio for subjects who differ by one unit with respect to the covariate.
9 Fitting the Generalized Linear Model for the Alzheimer s Data in SAS We obtain parameter estimates for a generalized linear model using the method of maximum likelihood these estimates typically y cannot be computed in closed form. The following SAS program shows how to read the AD data into SAS, and then obtain a fit for the regression coefficients in the model of Example VI.A. options ls=79 nodate; data; input e4 ad count; cards; ;; proc genmod descending; model ad=e4 / dis=bin link=logit type3; weight count; run; proc sort; by descending ad descending e4; run; f proc freq order=data; tables e4*ad / chisq relrisk; weight count; run;
10 The FREQ Procedure SAS Output Stat 5100 Linear Regression and Time Series Table of e4 by ad e4 ad Frequency Percent Row Pct Col Pct 1 0 Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total Statistics for Table of e4 by ad Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ChiSquare <.0001 Likelihood Ratio ChiSquare <.0001 Continuity Adj. ChiSquare <.0001 MantelHaenszel ChiSquare <.0001 Phi Coefficient Contingency Coefficient Cramer's V
11 SAS Output (cont d) Stat 5100 Linear Regression and Time Series Fisher's Exact Test ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cell (1,1) Frequency (F) 308 Leftsided Pr <= F Rightsided id d Pr >= F 3.366E30366E 30 Table Probability (P) 6.085E30 Twosided Pr <= P 4.889E30 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ CaseControl (Odds Ratio) Cohort (Col1 Risk) Cohort (Col2 Risk)
12 The GENMOD Procedure Model Information SAS Output (cont d) Data Set WORK.DATA1 Distribution Binomial Link Function Logit Dependent Variable ad Scale Weight Variable count Number of Observations Read 4 Number of Observations Used 4 Sum of Weights 4962 Number of Events 2 Number of Trials 4 Response Profile Ordered Total Value ad Frequency PROC GENMOD is modeling the probability that ad='1'. Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance Scaled Deviance Pearson ChiSquare Scaled Pearson X Log Likelihood Algorithm converged. Stat 5100 Linear Regression and Time Series
13 SAS Output (cont d) Stat 5100 Linear Regression and Time Series Analysis Of Parameter Estimates Standard Wald 95% Chi Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept < 0001 Intercept <.0001 e <.0001 Scale
14 Example VI.A (cont d) The SAS output t indicates that t ˆ and ˆ According to the fit of the regression model, what are the estimated log odds of AD for someone with no APOE ε4 allele? What are the estimated log odds given for someone with at least one highrisk allele? Wh t i th ti t d l dd ti f AD i k i 4 What is the estimated log odds ratio of AD risk comparing ε4 carriers to noncarriers? How does this estimate compare with the sample odds ratio computed using the data in the 2 x 2 table?
Basic Statistical and Modeling Procedures Using SAS
Basic Statistical and Modeling Procedures Using SAS OneSample Tests The statistical procedures illustrated in this handout use two datasets. The first, Pulse, has information collected in a classroom
More informationUsing 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 informationSAS 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 informationBeginning Tutorials. PROC FREQ: It s More Than Counts Richard Severino, The Queen s Medical Center, Honolulu, HI OVERVIEW.
Paper 6925 PROC FREQ: It s More Than Counts Richard Severino, The Queen s Medical Center, Honolulu, HI ABSTRACT The FREQ procedure can be used for more than just obtaining a simple frequency distribution
More informationLecture 12: Generalized Linear Models for Binary Data
Lecture 12: Generalized Linear Models for Binary Data Dipankar Bandyopadhyay, Ph.D. BMTRY 711: Analysis of Categorical Data Spring 2011 Division of Biostatistics and Epidemiology Medical University of
More informationLecture 14: GLM Estimation and Logistic Regression
Lecture 14: GLM Estimation and Logistic Regression Dipankar Bandyopadhyay, Ph.D. BMTRY 711: Analysis of Categorical Data Spring 2011 Division of Biostatistics and Epidemiology Medical University of South
More informationOverview Classes. 123 Logistic regression (5) 193 Building and applying logistic regression (6) 263 Generalizations of logistic regression (7)
Overview Classes 123 Logistic regression (5) 193 Building and applying logistic regression (6) 263 Generalizations of logistic regression (7) 24 Loglinear models (8) 54 1517 hrs; 5B02 Building and
More informationLecture 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 information11. Analysis of Casecontrol Studies Logistic Regression
Research methods II 113 11. Analysis of Casecontrol Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationGeneralized 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 informationStatistics, Data Analysis & Econometrics
Using the LOGISTIC Procedure to Model Responses to Financial Services Direct Marketing David Marsh, Senior Credit Risk Modeler, Canadian Tire Financial Services, Welland, Ontario ABSTRACT It is more important
More informationGuido s Guide to PROC FREQ A Tutorial for Beginners Using the SAS System Joseph J. Guido, University of Rochester Medical Center, Rochester, NY
Guido s Guide to PROC FREQ A Tutorial for Beginners Using the SAS System Joseph J. Guido, University of Rochester Medical Center, Rochester, NY ABSTRACT PROC FREQ is an essential procedure within BASE
More information5. 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. HosmerLemeshow test for lack of fit 5. Ordinal regression: cumulative categories proportional
More informationLogit 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 informationAbbas S. Tavakoli, DrPH, MPH, ME 1 ; Nikki R. Wooten, PhD, LISWCP 2,3, Jordan Brittingham, MSPH 4
1 Paper 16802016 Using GENMOD to Analyze Correlated Data on Military System Beneficiaries Receiving Inpatient Behavioral Care in South Carolina Care Systems Abbas S. Tavakoli, DrPH, MPH, ME 1 ; Nikki
More informationMultinomial 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 informationChapter 29 The GENMOD Procedure. Chapter Table of Contents
Chapter 29 The GENMOD Procedure Chapter Table of Contents OVERVIEW...1365 WhatisaGeneralizedLinearModel?...1366 ExamplesofGeneralizedLinearModels...1367 TheGENMODProcedure...1368 GETTING STARTED...1370
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 SigmaRestricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More informationLecture 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 informationOrdinal 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 information13. 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 informationLogistic 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 informationTwo 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 informationPoisson Models for Count Data
Chapter 4 Poisson Models for Count Data In this chapter we study loglinear models for count data under the assumption of a Poisson error structure. These models have many applications, not only to the
More informationExamples 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 informationUnit 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 2way tables Adds capability studying several predictors, but Limited to
More informationPoisson Regression or Regression of Counts (& Rates)
Poisson Regression or Regression of (& Rates) Carolyn J. Anderson Department of Educational Psychology University of Illinois at UrbanaChampaign Generalized Linear Models Slide 1 of 51 Outline Outline
More informationThe 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, 164169 1538 9472/13/$95.00 The Probit Link Function in Generalized Linear Models for Data Mining Applications
More informationLogistic 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 informationModels 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 extrapoisson variation and the negative binomial model, with brief appearances
More informationCommon Univariate and Bivariate Applications of the Chisquare Distribution
Common Univariate and Bivariate Applications of the Chisquare Distribution The probability density function defining the chisquare distribution is given in the chapter on Chisquare in Howell's text.
More informationThis can dilute the significance of a departure from the null hypothesis. We can focus the test on departures of a particular form.
OneDegreeofFreedom Tests Test for group occasion interactions has (number of groups 1) number of occasions 1) degrees of freedom. This can dilute the significance of a departure from the null hypothesis.
More informationData Mining and Data Warehousing. Henryk Maciejewski. Data Mining Predictive modelling: regression
Data Mining and Data Warehousing Henryk Maciejewski Data Mining Predictive modelling: regression Algorithms for Predictive Modelling Contents Regression Classification Auxiliary topics: Estimation of prediction
More informationCool Tools for PROC LOGISTIC
Cool Tools for PROC LOGISTIC Paul D. Allison Statistical Horizons LLC and the University of Pennsylvania March 2013 www.statisticalhorizons.com 1 New Features in LOGISTIC ODDSRATIO statement EFFECTPLOT
More informationSimple 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 information1. 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 1propZint 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 informationBivariate Statistics Session 2: Measuring Associations ChiSquare Test
Bivariate Statistics Session 2: Measuring Associations ChiSquare Test Features Of The ChiSquare Statistic The chisquare test is nonparametric. That is, it makes no assumptions about the distribution
More informationSUGI 29 Statistics and Data Analysis
Paper 19429 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 informationI L L I N O I S UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
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 URBANACHAMPAIGN Linear Algebra Slide 1 of
More informationABSTRACT INTRODUCTION
Paper SP032009 Illustrative Logistic Regression Examples using PROC LOGISTIC: New Features in SAS/STAT 9.2 Robert G. Downer, Grand Valley State University, Allendale, MI Patrick J. Richardson, Van Andel
More informationGeneralized 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 informationDiscrete Distributions
Discrete Distributions Chapter 1 11 Introduction 1 12 The Binomial Distribution 2 13 The Poisson Distribution 8 14 The Multinomial Distribution 11 15 Negative Binomial and Negative Multinomial Distributions
More informationA Tutorial on Logistic Regression
A Tutorial on Logistic Regression Ying So, SAS Institute Inc., Cary, NC ABSTRACT Many procedures in SAS/STAT can be used to perform logistic regression analysis: CATMOD, GENMOD,LOGISTIC, and PROBIT. Each
More informationLatent Class Regression Part II
This work is licensed under a Creative Commons AttributionNonCommercialShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationDeveloping 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 informationLecture 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 informationRegression with a Binary Dependent Variable
Regression with a Binary Dependent Variable Chapter 9 Michael Ash CPPA Lecture 22 Course Notes Endgame Takehome final Distributed Friday 19 May Due Tuesday 23 May (Paper or emailed PDF ok; no Word, Excel,
More informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationCategorical Data Analysis
Richard L. Scheaffer University of Florida The reference material and many examples for this section are based on Chapter 8, Analyzing Association Between Categorical Variables, from Statistical Methods
More informationTopic 19: Goodness of Fit
Topic 19: November 24, 2009 A goodness of fit test examine the case of a sequence if independent experiments each of which can have 1 of k possible outcomes. In terms of hypothesis testing, let π = (π
More informationMATH4427 Notebook 2 Spring 2016. 2 MATH4427 Notebook 2 3. 2.1 Definitions and Examples... 3. 2.2 Performance Measures for Estimators...
MATH4427 Notebook 2 Spring 2016 prepared by Professor Jenny Baglivo c Copyright 20092016 by Jenny A. Baglivo. All Rights Reserved. Contents 2 MATH4427 Notebook 2 3 2.1 Definitions and Examples...................................
More informationLinda 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 informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep 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 informationLogistic regression: Model selection
Logistic regression: April 14 The WCGS data Measures of predictive power Today we will look at issues of model selection and measuring the predictive power of a model in logistic regression Our data set
More informationModel Fitting in PROC GENMOD Jean G. Orelien, Analytical Sciences, Inc.
Paper 26426 Model Fitting in PROC GENMOD Jean G. Orelien, Analytical Sciences, Inc. Abstract: There are several procedures in the SAS System for statistical modeling. Most statisticians who use the SAS
More informationln(p/(1p)) = α +β*age35plus, where p is the probability or odds of drinking
Dummy Coding for Dummies Kathryn Martin, Maternal, Child and Adolescent Health Program, California Department of Public Health ABSTRACT There are a number of ways to incorporate categorical variables into
More informationChapter 39 The LOGISTIC Procedure. Chapter Table of Contents
Chapter 39 The LOGISTIC Procedure Chapter Table of Contents OVERVIEW...1903 GETTING STARTED...1906 SYNTAX...1910 PROCLOGISTICStatement...1910 BYStatement...1912 CLASSStatement...1913 CONTRAST Statement.....1916
More informationUsing 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 informationMultivariate 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 informationSAS Syntax and Output for Data Manipulation:
Psyc 944 Example 5 page 1 Practice with Fixed and Random Effects of Time in Modeling WithinPerson Change The models for this example come from Hoffman (in preparation) chapter 5. We will be examining
More informationProbability Calculator
Chapter 95 Introduction Most statisticians have a set of probability tables that they refer to in doing their statistical wor. This procedure provides you with a set of electronic statistical tables that
More informationStatistics 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 informationBasic 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 information5 Modeling Survival Data with Parametric Regression
5 Modeling Survival Data with Parametric Regression Models 5. The Accelerated Failure Time Model Before talking about parametric regression models for survival data, let us introduce the accelerated failure
More informationUsing Stata for Categorical Data Analysis
Using Stata for Categorical Data Analysis NOTE: These problems make extensive use of Nick Cox s tab_chi, which is actually a collection of routines, and Adrian Mander s ipf command. From within Stata,
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
More informationHow to set the main menu of STATA to default factory settings standards
University of Pretoria Data analysis for evaluation studies Examples in STATA version 11 List of data sets b1.dta (To be created by students in class) fp1.xls (To be provided to students) fp1.txt (To be
More informationA Handbook of Statistical Analyses Using R. Brian S. Everitt and Torsten Hothorn
A Handbook of Statistical Analyses Using R Brian S. Everitt and Torsten Hothorn CHAPTER 6 Logistic Regression and Generalised Linear Models: Blood Screening, Women s Role in Society, and Colonic Polyps
More informationLOGISTIC REGRESSION. Nitin R Patel. where the dependent variable, y, is binary (for convenience we often code these values as
LOGISTIC REGRESSION Nitin R Patel Logistic regression extends the ideas of multiple linear regression to the situation where the dependent variable, y, is binary (for convenience we often code these values
More informationModule 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 } OneSample ChiSquare Test
More informationExamining a Fitted Logistic Model
STAT 536 Lecture 16 1 Examining a Fitted Logistic Model Deviance Test for Lack of Fit The data below describes the male birth fraction male births/total births over the years 1931 to 1990. A simple logistic
More informationPoint Biserial Correlation Tests
Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the productmoment correlation calculated between a continuous random variable
More informationPredicting the US Presidential Approval and Applying the Model to Foreign Countries.
Predicting the US Presidential Approval and Applying the Model to Foreign Countries. Author: Daniel Mariani Date: May 01, 2013 Thesis Advisor: Dr. Samanta ABSTRACT Economic factors play a significant,
More informationOutline. Topic 4  Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4  Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test  Fall 2013 R 2 and the coefficient of correlation
More informationPROC LOGISTIC: Traps for the unwary Peter L. Flom, Independent statistical consultant, New York, NY
PROC LOGISTIC: Traps for the unwary Peter L. Flom, Independent statistical consultant, New York, NY ABSTRACT Keywords: Logistic. INTRODUCTION This paper covers some gotchas in SAS R PROC LOGISTIC. A gotcha
More informationCHAPTER 3 EXAMPLES: REGRESSION AND PATH ANALYSIS
Examples: Regression And Path Analysis CHAPTER 3 EXAMPLES: REGRESSION AND PATH ANALYSIS Regression analysis with univariate or multivariate dependent variables is a standard procedure for modeling relationships
More informationLogit and Probit. Brad Jones 1. April 21, 2009. University of California, Davis. Bradford S. Jones, UCDavis, 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 informationRegression 3: Logistic Regression
Regression 3: Logistic Regression Marco Baroni Practical Statistics in R Outline Logistic regression Logistic regression in R Outline Logistic regression Introduction The model Looking at and comparing
More informationChapter 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 informationADVANCED FORECASTING MODELS USING SAS SOFTWARE
ADVANCED FORECASTING MODELS USING SAS SOFTWARE Girish Kumar Jha IARI, Pusa, New Delhi 110 012 gjha_eco@iari.res.in 1. Transfer Function Model Univariate ARIMA models are useful for analysis and forecasting
More informationStatistical 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 informationSUMAN DUVVURU STAT 567 PROJECT REPORT
SUMAN DUVVURU STAT 567 PROJECT REPORT SURVIVAL ANALYSIS OF HEROIN ADDICTS Background and introduction: Current illicit drug use among teens is continuing to increase in many countries around the world.
More informationExample: 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 informationStatistical Functions in Excel
Statistical Functions in Excel There are many statistical functions in Excel. Moreover, there are other functions that are not specified as statistical functions that are helpful in some statistical analyses.
More informationLogistic 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 informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationGamma Distribution Fitting
Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics
More informationLOGIT 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 information1.1. Simple Regression in Excel (Excel 2010).
.. Simple Regression in Excel (Excel 200). To get the Data Analysis tool, first click on File > Options > AddIns > Go > Select Data Analysis Toolpack & Toolpack VBA. Data Analysis is now available under
More informationYiming 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 informationGEEs: SAS Syntax and Examples
GEEs: SAS Syntax and Examples The repeated statement is used in genmod to fit GLMs by GEE. The format of the repeated statement is given by: repeated subject= subjecteffect/options;, where subjecteffect
More informationLogistic Models in R
Logistic Models in R Jim Bentley 1 Sample Data The following code reads the titanic data that we will use in our examples. > titanic = read.csv( + "http://bulldog2.redlands.edu/facultyfolder/jim_bentley/downloads/math111/titanic.csv
More informationLogistic 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 informationStatistics and Data Analysis
NESUG 27 PRO LOGISTI: The Logistics ehind Interpreting ategorical Variable Effects Taylor Lewis, U.S. Office of Personnel Management, Washington, D STRT The goal of this paper is to demystify how SS models
More informationLinear 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 informationWeek 5: Multiple Linear Regression
BUS41100 Applied Regression Analysis Week 5: Multiple Linear Regression Parameter estimation and inference, forecasting, diagnostics, dummy variables Robert B. Gramacy The University of Chicago Booth School
More informationWeight 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 informationModule 14: Missing Data Stata Practical
Module 14: Missing Data Stata Practical Jonathan Bartlett & James Carpenter London School of Hygiene & Tropical Medicine www.missingdata.org.uk Supported by ESRC grant RES 189250103 and MRC grant G0900724
More informationLOGISTIC 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 informationA New Effect Modification P Value Test Demonstrated. Manoj B. Agravat, MPH, University of South Florida, SESUG 2009
Paper SD018 A New Effect Modification P Value Test Demonstrated Manoj B. Agravat, MPH, University of South Florida, SESUG 2009 Abstract: Effect modification P value is a method to determine if there is
More information