Q30b Moyale Observed counts. The FREQ Procedure. Table 1 of type by response. Controlling for site=moyale. Improved (1+2) Same (3) Group only

Size: px
Start display at page:

Download "Q30b Moyale Observed counts. The FREQ Procedure. Table 1 of type by response. Controlling for site=moyale. Improved (1+2) Same (3) Group only"

Transcription

1 Moyale Observed counts 12:28 Thursday, December 01, The FREQ Procedure Table 1 of by Controlling for site=moyale Row Pct Improved (1+2) Same () Worsened (4+5) Group only Group + IBAR Loan Control

2 Moyale Using observed counts with zero counts incremented by 1, to "fix" zeros 12:28 Thursday, December 01, Model Information Data Set Distribution Link Function Dependent Variable Weight Variable WORK.QB Multinomial Cumulative Logit new2count Number of Observations Read 9 Number of Observations Used 9 Sum of Frequencies Read 91 Sum of Frequencies Used 91 Class Level Information Class site Levels Values 1 Moyale Group only Group + IBAR Loan Control Improved (1+2) Same () Worsened (4+5) Response Profile Ordered Value 1 Improved (1+2) 9 2 Same () 12 Worsened (4+5) 40 PROC GENMOD is modeling the probabilities of levels of having LOWER Ordered Values in the profile table. One way to change this to model the probabilities of HIGHER Ordered Values is to specify the DESCENDING option in the PROC statement. Parameter Information Parameter Effect Prm1 Group only Prm2 Group + IBAR Loan Prm Control Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood Algorithm converged.

3 Moyale Using observed counts with zero counts incremented by 1, to "fix" zeros 12:28 Thursday, December 01, 2011 Analysis Of Parameter Estimates Parameter DF Estimate Error Wald 95% Confidence Limits Chi-Square Pr > ChiSq Intercept Intercept Group only Group + IBAR Loan Control Scale The scale parameter was held fixed. LR Statistics For Type 1 Analysis Source Deviance DF Chi-Square Pr > ChiSq Intercepts Contrast Estimate Results Label Estimate Error Alpha Confidence Limits Chi-Square Pr > ChiSq LogOR Exp(LogOR12) LogOR Exp(LogOR1) LogOR Exp(LogOR2)

4 Liben Observed counts 12:28 Thursday, December 01, The FREQ Procedure Table 1 of by Controlling for site=liben Row Pct Improved (1+2) Same () Worsened (4+5) Group only Group + IBAR Loan Control

5 Liben Using observed counts, including zeros 12:28 Thursday, December 01, Model Information Data Set Distribution Link Function Dependent Variable Weight Variable WORK.QB Multinomial Cumulative Logit count Number of Observations Read 9 Number of Observations Used 9 Sum of Frequencies Read 90 Sum of Frequencies Used 90 Class Level Information Class site Levels Values 1 Liben Group only Group + IBAR Loan Control Improved (1+2) Same () Worsened (4+5) Response Profile Ordered Value 1 Improved (1+2) 50 2 Same () 2 Worsened (4+5) 17 PROC GENMOD is modeling the probabilities of levels of having LOWER Ordered Values in the profile table. One way to change this to model the probabilities of HIGHER Ordered Values is to specify the DESCENDING option in the PROC statement. Parameter Information Parameter Effect Prm1 Group only Prm2 Group + IBAR Loan Prm Control Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood Algorithm converged.

6 Liben Using observed counts, including zeros 12:28 Thursday, December 01, Analysis Of Parameter Estimates Parameter DF Estimate Error Wald 95% Confidence Limits Chi-Square Pr > ChiSq Intercept Intercept Group only <.0001 Group + IBAR Loan <.0001 Control Scale The scale parameter was held fixed. LR Statistics For Type 1 Analysis Source Deviance DF Chi-Square Pr > ChiSq Intercepts <.0001 Contrast Estimate Results Label Estimate Error Alpha Confidence Limits Chi-Square Pr > ChiSq LogOR Exp(LogOR12) LogOR <.0001 Exp(LogOR1) LogOR <.0001 Exp(LogOR2)

You can specify the response in the form of a single variable or in the form of a ratio of two variables denoted events/trials.

You can specify the response in the form of a single variable or in the form of a ratio of two variables denoted events/trials. The GENMOD Procedure MODEL Statement MODEL response = < effects > < /options > ; MODEL events/trials = < effects > < /options > ; You can specify the response in the form of a single variable or in the

More information

Contrasting Marginal and Mixed Effects Models Recall: two approaches to handling dependence in Generalized Linear Models:

Contrasting Marginal and Mixed Effects Models Recall: two approaches to handling dependence in Generalized Linear Models: Contrasting Marginal and Mixed Effects Models Recall: two approaches to handling dependence in Generalized Linear Models: Marginal models: based on the consequences of dependence on estimating model parameters.

More information

ESTIMATE PROP. IMPAIRED PRE- AND POST-INTERVENTION FOR THIN LIQUID SWALLOW TASKS. The SURVEYFREQ Procedure

ESTIMATE PROP. IMPAIRED PRE- AND POST-INTERVENTION FOR THIN LIQUID SWALLOW TASKS. The SURVEYFREQ Procedure ESTIMATE PROP. IMPAIRED PRE- AND POST-INTERVENTION FOR THIN LIQUID SWALLOW TASKS 18:58 Sunday, July 26, 2015 1 The SURVEYFREQ Procedure Data Summary Number of Clusters 30 Number of Observations 360 time_cat

More information

Poisson Data. Handout #4

Poisson Data. Handout #4 Poisson Data The other response variable of interest records the number of blue spots observed after incubation. This type of data, i.e. count data, is often skewed showing numerous small values with occasional

More information

Logistic Regression. Interpretation of linear regression. Other types of outcomes. 0-1 response variable: Wound infection. Usual linear regression

Logistic Regression. Interpretation of linear regression. Other types of outcomes. 0-1 response variable: Wound infection. Usual linear regression Logistic Regression Usual linear regression (repetition) y i = b 0 + b 1 x 1i + b 2 x 2i + e i, e i N(0,σ 2 ) or: y i N(b 0 + b 1 x 1i + b 2 x 2i,σ 2 ) Example (DGA, p. 336): E(PEmax) = 47.355 + 1.024

More information

ST3241 Categorical Data Analysis I Multicategory Logit Models. Logit Models For Nominal Responses

ST3241 Categorical Data Analysis I Multicategory Logit Models. Logit Models For Nominal Responses ST3241 Categorical Data Analysis I Multicategory Logit Models Logit Models For Nominal Responses 1 Models For Nominal Responses Y is nominal with J categories. Let {π 1,, π J } denote the response probabilities

More information

Analysis of Count Data A Business Perspective. George J. Hurley Sr. Research Manager The Hershey Company Milwaukee June 2013

Analysis of Count Data A Business Perspective. George J. Hurley Sr. Research Manager The Hershey Company Milwaukee June 2013 Analysis of Count Data A Business Perspective George J. Hurley Sr. Research Manager The Hershey Company Milwaukee June 2013 Overview Count data Methods Conclusions 2 Count data Count data Anything with

More information

Homework 5: Answer Key. Plausible Model: E(y) = µt. The expected number of arrests arrests equals a constant times the number who attend the game.

Homework 5: Answer Key. Plausible Model: E(y) = µt. The expected number of arrests arrests equals a constant times the number who attend the game. EdPsych/Psych/Soc 589 C.J. Anderson Homework 5: Answer Key 1. Probelm 3.18 (page 96 of Agresti). (a) Y assume Poisson random variable. Plausible Model: E(y) = µt. The expected number of arrests arrests

More information

Models for Binary Outcomes

Models for Binary Outcomes Models for Binary Outcomes Introduction The simple or binary response (for example, success or failure) analysis models the relationship between a binary response variable and one or more explanatory variables.

More information

COMPLEMENTARY LOG-LOG MODEL

COMPLEMENTARY LOG-LOG MODEL COMPLEMENTARY LOG-LOG MODEL Under the assumption of binary response, there are two alternatives to logit model: probit model and complementary-log-log model. They all follow the same form π ( x) =Φ ( α

More information

The GENMOD Procedure. Overview. Getting Started. Syntax. Details. Examples. References. SAS/STAT User's Guide. Book Contents Previous Next

The GENMOD Procedure. Overview. Getting Started. Syntax. Details. Examples. References. SAS/STAT User's Guide. Book Contents Previous Next Book Contents Previous Next SAS/STAT User's Guide Overview Getting Started Syntax Details Examples References Book Contents Previous Next Top http://v8doc.sas.com/sashtml/stat/chap29/index.htm29/10/2004

More information

Some comments on Partitioning

Some comments on Partitioning Some comments on Partitioning Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM 1/30 Partitioning Chi-Squares We have developed tests

More information

STA6938-Logistic Regression Model

STA6938-Logistic Regression Model Dr. Ying Zhang STA6938-Logistic Regression Model Topic 2-Multiple Logistic Regression Model Outlines:. Model Fitting 2. Statistical Inference for Multiple Logistic Regression Model 3. Interpretation of

More information

Logistic regression analysis. Birthe Lykke Thomsen H. Lundbeck A/S

Logistic regression analysis. Birthe Lykke Thomsen H. Lundbeck A/S Logistic regression analysis Birthe Lykke Thomsen H. Lundbeck A/S 1 Response with only two categories Example Odds ratio and risk ratio Quantitative explanatory variable More than one variable Logistic

More information

Multinomial Logistic Regression Models

Multinomial Logistic Regression Models Stat 544, Lecture 19 1 Multinomial Logistic Regression Models Polytomous responses. Logistic regression can be extended to handle responses that are polytomous, i.e. taking r>2 categories. (Note: The word

More information

Overdispersion Workshop in generalized linear models Uppsala, June 11-12, Outline. Overdispersion

Overdispersion Workshop in generalized linear models Uppsala, June 11-12, Outline. Overdispersion Biostokastikum Overdispersion is not uncommon in practice. In fact, some would maintain that overdispersion is the norm in practice and nominal dispersion the exception McCullagh and Nelder (1989) Overdispersion

More information

UNIVERSITY OF TORONTO. Faculty of Arts and Science APRIL 2010 EXAMINATIONS STA 303 H1S / STA 1002 HS. Duration - 3 hours. Aids Allowed: Calculator

UNIVERSITY OF TORONTO. Faculty of Arts and Science APRIL 2010 EXAMINATIONS STA 303 H1S / STA 1002 HS. Duration - 3 hours. Aids Allowed: Calculator UNIVERSITY OF TORONTO Faculty of Arts and Science APRIL 2010 EXAMINATIONS STA 303 H1S / STA 1002 HS Duration - 3 hours Aids Allowed: Calculator LAST NAME: FIRST NAME: STUDENT NUMBER: There are 27 pages

More information

Model Based Statistics in Biology. Part V. The Generalized Linear Model. Chapter 18.1 Logistic Regression (Dose - Response)

Model Based Statistics in Biology. Part V. The Generalized Linear Model. Chapter 18.1 Logistic Regression (Dose - Response) Model Based Statistics in Biology. Part V. The Generalized Linear Model. Logistic Regression ( - Response) ReCap. Part I (Chapters 1,2,3,4), Part II (Ch 5, 6, 7) ReCap Part III (Ch 9, 10, 11), Part IV

More information

Simple logistic regression

Simple logistic regression Simple logistic regression Biometry 755 Spring 2009 Simple logistic regression p. 1/47 Model assumptions 1. The observed data are independent realizations of a binary response variable Y that follows a

More information

Section Poisson Regression

Section Poisson Regression Section 14.13 Poisson Regression Timothy Hanson Department of Statistics, University of South Carolina Stat 705: Data Analysis II 1 / 26 Poisson regression Regular regression data {(x i, Y i )} n i=1,

More information

STA 303 H1S / 1002 HS Winter 2011 Test March 7, ab 1cde 2abcde 2fghij 3

STA 303 H1S / 1002 HS Winter 2011 Test March 7, ab 1cde 2abcde 2fghij 3 STA 303 H1S / 1002 HS Winter 2011 Test March 7, 2011 LAST NAME: FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 303 STA 1002 INSTRUCTIONS: Time: 90 minutes Aids allowed: calculator. Some formulae

More information

The GENMOD Procedure (Book Excerpt)

The GENMOD Procedure (Book Excerpt) SAS/STAT 9.22 User s Guide The GENMOD Procedure (Book Excerpt) SAS Documentation This document is an individual chapter from SAS/STAT 9.22 User s Guide. The correct bibliographic citation for the complete

More information

Testing Independence

Testing Independence Testing Independence Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM 1/50 Testing Independence Previously, we looked at RR = OR = 1

More information

Appendix: Computer Programs for Logistic Regression

Appendix: Computer Programs for Logistic Regression Appendix: Computer Programs for Logistic Regression In this appendix, we provide examples of computer programs to carry out unconditional logistic regression, conditional logistic regression, polytomous

More information

Class Notes: Week 8. Probit versus Logit Link Functions and Count Data

Class Notes: Week 8. Probit versus Logit Link Functions and Count Data Ronald Heck Class Notes: Week 8 1 Class Notes: Week 8 Probit versus Logit Link Functions and Count Data This week we ll take up a couple of issues. The first is working with a probit link function. While

More information

SAS/STAT 14.2 User s Guide. The GENMOD Procedure

SAS/STAT 14.2 User s Guide. The GENMOD Procedure SAS/STAT 14.2 User s Guide The GENMOD Procedure This document is an individual chapter from SAS/STAT 14.2 User s Guide. The correct bibliographic citation for this manual is as follows: SAS Institute Inc.

More information

Where have all the puffins gone 1. An Analysis of Atlantic Puffin (Fratercula arctica) Banding Returns in Newfoundland

Where have all the puffins gone 1. An Analysis of Atlantic Puffin (Fratercula arctica) Banding Returns in Newfoundland Where have all the puffins gone 1 An Analysis of Atlantic Puffin (Fratercula arctica) Banding Returns in Newfoundland Dave Fifield 1 With apologies to Pete Seeger. Introduction Seabirds are the most visible

More information

ANALYSING BINARY DATA IN A REPEATED MEASUREMENTS SETTING USING SAS

ANALYSING BINARY DATA IN A REPEATED MEASUREMENTS SETTING USING SAS Libraries 1997-9th Annual Conference Proceedings ANALYSING BINARY DATA IN A REPEATED MEASUREMENTS SETTING USING SAS Eleanor F. Allan Follow this and additional works at: http://newprairiepress.org/agstatconference

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

Chapter 14 Logistic and Poisson Regressions

Chapter 14 Logistic and Poisson Regressions STAT 525 SPRING 2018 Chapter 14 Logistic and Poisson Regressions Professor Min Zhang Logistic Regression Background In many situations, the response variable has only two possible outcomes Disease (Y =

More information

Sections 4.1, 4.2, 4.3

Sections 4.1, 4.2, 4.3 Sections 4.1, 4.2, 4.3 Timothy Hanson Department of Statistics, University of South Carolina Stat 770: Categorical Data Analysis 1/ 32 Chapter 4: Introduction to Generalized Linear Models Generalized linear

More information

Epidemiology Wonders of Biostatistics Chapter 13 - Effect Measures. John Koval

Epidemiology Wonders of Biostatistics Chapter 13 - Effect Measures. John Koval Epidemiology 9509 Wonders of Biostatistics Chapter 13 - Effect Measures John Koval Department of Epidemiology and Biostatistics University of Western Ontario What is being covered 1. risk factors 2. risk

More information

Wrap-up. The General Linear Model is a special case of the Generalized Linear Model. Consequently, we can carry out any GLM as a GzLM.

Wrap-up. The General Linear Model is a special case of the Generalized Linear Model. Consequently, we can carry out any GLM as a GzLM. Model Based Statistics in Biology. Part V. The Generalized Linear Model. Analysis of Continuous Data ReCap. Part I (Chapters 1,2,3,4), Part II (Ch 5, 6, 7) ReCap Part III (Ch 9, 10, 11), Part IV (Ch13,

More information

Regression Models for Risks(Proportions) and Rates. Proportions. E.g. [Changes in] Sex Ratio: Canadian Births in last 60 years

Regression Models for Risks(Proportions) and Rates. Proportions. E.g. [Changes in] Sex Ratio: Canadian Births in last 60 years Regression Models for Risks(Proportions) and Rates Proportions E.g. [Changes in] Sex Ratio: Canadian Births in last 60 years Parameter of Interest: (male)... just above 0.5 or (male)/ (female)... "ODDS"...

More information

Cohen s s Kappa and Log-linear Models

Cohen s s Kappa and Log-linear Models Cohen s s Kappa and Log-linear Models HRP 261 03/03/03 10-11 11 am 1. Cohen s Kappa Actual agreement = sum of the proportions found on the diagonals. π ii Cohen: Compare the actual agreement with the chance

More information

Case-control studies C&H 16

Case-control studies C&H 16 Case-control studies C&H 6 Bendix Carstensen Steno Diabetes Center & Department of Biostatistics, University of Copenhagen bxc@steno.dk http://bendixcarstensen.com PhD-course in Epidemiology, Department

More information

Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study

Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study 1.4 0.0-6 7 8 9 10 11 12 13 14 15 16 17 18 19 age Model 1: A simple broken stick model with knot at 14 fit with

More information

Ch 6: Multicategory Logit Models

Ch 6: Multicategory Logit Models 293 Ch 6: Multicategory Logit Models Y has J categories, J>2. Extensions of logistic regression for nominal and ordinal Y assume a multinomial distribution for Y. In R, we will fit these models using the

More information

UNIVERSITY OF MASSACHUSETTS Department of Mathematics and Statistics Applied Statistics Friday, January 15, 2016

UNIVERSITY OF MASSACHUSETTS Department of Mathematics and Statistics Applied Statistics Friday, January 15, 2016 UNIVERSITY OF MASSACHUSETTS Department of Mathematics and Statistics Applied Statistics Friday, January 15, 2016 Work all problems. 60 points are needed to pass at the Masters Level and 75 to pass at the

More information

BIOS 625 Fall 2015 Homework Set 3 Solutions

BIOS 625 Fall 2015 Homework Set 3 Solutions BIOS 65 Fall 015 Homework Set 3 Solutions 1. Agresti.0 Table.1 is from an early study on the death penalty in Florida. Analyze these data and show that Simpson s Paradox occurs. Death Penalty Victim's

More information

BMI 541/699 Lecture 22

BMI 541/699 Lecture 22 BMI 541/699 Lecture 22 Where we are: 1. Introduction and Experimental Design 2. Exploratory Data Analysis 3. Probability 4. T-based methods for continous variables 5. Power and sample size for t-based

More information

Chapter 5: Logistic Regression-I

Chapter 5: Logistic Regression-I : Logistic Regression-I Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM [Acknowledgements to Tim Hanson and Haitao Chu] D. Bandyopadhyay

More information

Changes Report 2: Examples from the Australian Longitudinal Study on Women s Health for Analysing Longitudinal Data

Changes Report 2: Examples from the Australian Longitudinal Study on Women s Health for Analysing Longitudinal Data ChangesReport: ExamplesfromtheAustralianLongitudinal StudyonWomen shealthforanalysing LongitudinalData June005 AustralianLongitudinalStudyonWomen shealth ReporttotheDepartmentofHealthandAgeing ThisreportisbasedonthecollectiveworkoftheStatisticsGroupoftheAustralianLongitudinal

More information

ssh tap sas913, sas https://www.statlab.umd.edu/sasdoc/sashtml/onldoc.htm

ssh tap sas913, sas https://www.statlab.umd.edu/sasdoc/sashtml/onldoc.htm Kedem, STAT 430 SAS Examples: Logistic Regression ==================================== ssh abc@glue.umd.edu, tap sas913, sas https://www.statlab.umd.edu/sasdoc/sashtml/onldoc.htm a. Logistic regression.

More information

6 Applying Logistic Regression Models

6 Applying Logistic Regression Models 6 Applying Logistic Regression Models I Model Selection and Diagnostics I.1 Model Selection # of x s can be entered in the model: Rule of thumb: # of events (both [Y = 1] and [Y = 0]) per x 10. Need to

More information

Deriving Decision Rules

Deriving Decision Rules Deriving Decision Rules Jonathan Yuen Department of Forest Mycology and Pathology Swedish University of Agricultural Sciences email: Jonathan.Yuen@mykopat.slu.se telephone (018) 672369 May 17, 2006 Yuen,

More information

ST3241 Categorical Data Analysis I Logistic Regression. An Introduction and Some Examples

ST3241 Categorical Data Analysis I Logistic Regression. An Introduction and Some Examples ST3241 Categorical Data Analysis I Logistic Regression An Introduction and Some Examples 1 Business Applications Example Applications The probability that a subject pays a bill on time may use predictors

More information

SAS Analysis Examples Replication C8. * SAS Analysis Examples Replication for ASDA 2nd Edition * Berglund April 2017 * Chapter 8 ;

SAS Analysis Examples Replication C8. * SAS Analysis Examples Replication for ASDA 2nd Edition * Berglund April 2017 * Chapter 8 ; SAS Analysis Examples Replication C8 * SAS Analysis Examples Replication for ASDA 2nd Edition * Berglund April 2017 * Chapter 8 ; libname ncsr "P:\ASDA 2\Data sets\ncsr\" ; data c8_ncsr ; set ncsr.ncsr_sub_13nov2015

More information

Model Estimation Example

Model Estimation Example Ronald H. Heck 1 EDEP 606: Multivariate Methods (S2013) April 7, 2013 Model Estimation Example As we have moved through the course this semester, we have encountered the concept of model estimation. Discussions

More information

Lecture 12: Effect modification, and confounding in logistic regression

Lecture 12: Effect modification, and confounding in logistic regression Lecture 12: Effect modification, and confounding in logistic regression Ani Manichaikul amanicha@jhsph.edu 4 May 2007 Today Categorical predictor create dummy variables just like for linear regression

More information

Longitudinal Modeling with Logistic Regression

Longitudinal Modeling with Logistic Regression Newsom 1 Longitudinal Modeling with Logistic Regression Longitudinal designs involve repeated measurements of the same individuals over time There are two general classes of analyses that correspond to

More information

NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION. ST3241 Categorical Data Analysis. (Semester II: ) April/May, 2011 Time Allowed : 2 Hours

NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION. ST3241 Categorical Data Analysis. (Semester II: ) April/May, 2011 Time Allowed : 2 Hours NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION Categorical Data Analysis (Semester II: 2010 2011) April/May, 2011 Time Allowed : 2 Hours Matriculation No: Seat No: Grade Table Question 1 2 3 4 5 6 Full marks

More information

Review of Multinomial Distribution If n trials are performed: in each trial there are J > 2 possible outcomes (categories) Multicategory Logit Models

Review of Multinomial Distribution If n trials are performed: in each trial there are J > 2 possible outcomes (categories) Multicategory Logit Models Chapter 6 Multicategory Logit Models Response Y has J > 2 categories. Extensions of logistic regression for nominal and ordinal Y assume a multinomial distribution for Y. 6.1 Logit Models for Nominal Responses

More information

A course in statistical modelling. session 09: Modelling count variables

A course in statistical modelling. session 09: Modelling count variables A Course in Statistical Modelling SEED PGR methodology training December 08, 2015: 12 2pm session 09: Modelling count variables Graeme.Hutcheson@manchester.ac.uk blackboard: RSCH80000 SEED PGR Research

More information

Chapter 11: Analysis of matched pairs

Chapter 11: Analysis of matched pairs Chapter 11: Analysis of matched pairs Timothy Hanson Department of Statistics, University of South Carolina Stat 770: Categorical Data Analysis 1 / 42 Chapter 11: Models for Matched Pairs Example: Prime

More information

Chapter 4: Generalized Linear Models-II

Chapter 4: Generalized Linear Models-II : Generalized Linear Models-II Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM [Acknowledgements to Tim Hanson and Haitao Chu] D. Bandyopadhyay

More information

Chapter 11: Models for Matched Pairs

Chapter 11: Models for Matched Pairs : Models for Matched Pairs Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM [Acknowledgements to Tim Hanson and Haitao Chu] D. Bandyopadhyay

More information

STAT 5200 Handout #23. Repeated Measures Example (Ch. 16)

STAT 5200 Handout #23. Repeated Measures Example (Ch. 16) Motivating Example: Glucose STAT 500 Handout #3 Repeated Measures Example (Ch. 16) An experiment is conducted to evaluate the effects of three diets on the serum glucose levels of human subjects. Twelve

More information

Department of Mathematics The University of Toledo. Master of Science Degree Comprehensive Examination Applied Statistics.

Department of Mathematics The University of Toledo. Master of Science Degree Comprehensive Examination Applied Statistics. Department of Mathematics The University of Toledo Master of Science Degree Comprehensive Examination Applied Statistics April 8, 205 nstructions Do all problems. Show all of your computations. Prove all

More information

Inference for Binomial Parameters

Inference for Binomial Parameters Inference for Binomial Parameters Dipankar Bandyopadhyay, Ph.D. Department of Biostatistics, Virginia Commonwealth University D. Bandyopadhyay (VCU) BIOS 625: Categorical Data & GLM 1 / 58 Inference for

More information

Chapter 2. Appendix A: Vertical line model parameter estimates

Chapter 2. Appendix A: Vertical line model parameter estimates Chapter 2 Appendix A: Vertical line model parameter estimates 1 Model Summary Model Variables 4 Parameters 166 Equations 4 Number of Statements 252 Note: The parameter beta12 is shared by 2 of the equations

More information

8 Nominal and Ordinal Logistic Regression

8 Nominal and Ordinal Logistic Regression 8 Nominal and Ordinal Logistic Regression 8.1 Introduction If the response variable is categorical, with more then two categories, then there are two options for generalized linear models. One relies on

More information

STAT 705: Analysis of Contingency Tables

STAT 705: Analysis of Contingency Tables STAT 705: Analysis of Contingency Tables Timothy Hanson Department of Statistics, University of South Carolina Stat 705: Analysis of Contingency Tables 1 / 45 Outline of Part I: models and parameters Basic

More information

Example 7b: Generalized Models for Ordinal Longitudinal Data using SAS GLIMMIX, STATA MEOLOGIT, and MPLUS (last proportional odds model only)

Example 7b: Generalized Models for Ordinal Longitudinal Data using SAS GLIMMIX, STATA MEOLOGIT, and MPLUS (last proportional odds model only) CLDP945 Example 7b page 1 Example 7b: Generalized Models for Ordinal Longitudinal Data using SAS GLIMMIX, STATA MEOLOGIT, and MPLUS (last proportional odds model only) This example comes from real data

More information

Generalized linear models

Generalized linear models Generalized linear models Douglas Bates November 01, 2010 Contents 1 Definition 1 2 Links 2 3 Estimating parameters 5 4 Example 6 5 Model building 8 6 Conclusions 8 7 Summary 9 1 Generalized Linear Models

More information

A course in statistical modelling. session 06b: Modelling count data

A course in statistical modelling. session 06b: Modelling count data A Course in Statistical Modelling University of Glasgow 29 and 30 January, 2015 session 06b: Modelling count data Graeme Hutcheson 1 Luiz Moutinho 2 1 Manchester Institute of Education Manchester university

More information

EVALUATION OF WILDLIFE REFLECTORS IN REDUCING VEHICLE-DEER COLLISIONS ON INDIANA INTERSTATE 80/90

EVALUATION OF WILDLIFE REFLECTORS IN REDUCING VEHICLE-DEER COLLISIONS ON INDIANA INTERSTATE 80/90 Final Report FHWA/IN/JTRP-2006/18 EVALUATION OF WILDLIFE REFLECTORS IN REDUCING VEHICLE-DEER COLLISIONS ON INDIANA INTERSTATE 80/90 By Sedat Gulen Statistical Pavement Research Engineer Division of Research

More information

Logistic Regression for Ordinal Responses

Logistic Regression for Ordinal Responses Logistic Regression for Ordinal Responses Edps/Psych/Soc 589 Carolyn J. Anderson Department of Educational Psychology c Board of Trustees, University of Illinois Fall 2018 Outline Common models for ordinal

More information

Count data page 1. Count data. 1. Estimating, testing proportions

Count data page 1. Count data. 1. Estimating, testing proportions Count data page 1 Count data 1. Estimating, testing proportions 100 seeds, 45 germinate. We estimate probability p that a plant will germinate to be 0.45 for this population. Is a 50% germination rate

More information

STAT 7030: Categorical Data Analysis

STAT 7030: Categorical Data Analysis STAT 7030: Categorical Data Analysis 5. Logistic Regression Peng Zeng Department of Mathematics and Statistics Auburn University Fall 2012 Peng Zeng (Auburn University) STAT 7030 Lecture Notes Fall 2012

More information

Confirmatory and Exploratory Data Analyses Using PROC GENMOD: Factors Associated with Red Light Running Crashes

Confirmatory and Exploratory Data Analyses Using PROC GENMOD: Factors Associated with Red Light Running Crashes Confirmatory and Exploratory Data Analyses Using PROC GENMOD: Factors Associated with Red Light Running Crashes Li wan Chen, LENDIS Corporation, McLean, VA Forrest Council, Highway Safety Research Center,

More information

An Introduction to the Analysis of Rare Events

An Introduction to the Analysis of Rare Events PharmaSUG - Paper AA- An Introduction to the Analysis of Rare Events Nate Derby, Stakana Analytics, Seattle, WA ABSTRACT Analyzing rare events like disease incidents, natural disasters, or component failures

More information

Faculty of Health Sciences. Correlated data. Count variables. Lene Theil Skovgaard & Julie Lyng Forman. December 6, 2016

Faculty of Health Sciences. Correlated data. Count variables. Lene Theil Skovgaard & Julie Lyng Forman. December 6, 2016 Faculty of Health Sciences Correlated data Count variables Lene Theil Skovgaard & Julie Lyng Forman December 6, 2016 1 / 76 Modeling count outcomes Outline The Poisson distribution for counts Poisson models,

More information

BIOMETRICS INFORMATION

BIOMETRICS INFORMATION BIOMETRICS INFORMATION (You re 95% likely to need this information) PAMPHLET NO. # 41 DATE: September 18, 1992 SUBJECT: Power Analysis and Sample Size Determination for Contingency Table Tests Statistical

More information

Logistic Regression Analyses in the Water Level Study

Logistic Regression Analyses in the Water Level Study Logistic Regression Analyses in the Water Level Study A. Introduction. 166 students participated in the Water level Study. 70 passed and 96 failed to correctly draw the water level in the glass. There

More information

Normal distribution We have a random sample from N(m, υ). The sample mean is Ȳ and the corrected sum of squares is S yy. After some simplification,

Normal distribution We have a random sample from N(m, υ). The sample mean is Ȳ and the corrected sum of squares is S yy. After some simplification, Likelihood Let P (D H) be the probability an experiment produces data D, given hypothesis H. Usually H is regarded as fixed and D variable. Before the experiment, the data D are unknown, and the probability

More information

Analysis of binary repeated measures data with R

Analysis of binary repeated measures data with R Analysis of binary repeated measures data with R Right-handed basketball players take right and left-handed shots from 3 locations in a different random order for each player. Hit or miss is recorded.

More information

Chapter 4: Generalized Linear Models-I

Chapter 4: Generalized Linear Models-I : Generalized Linear Models-I Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM [Acknowledgements to Tim Hanson and Haitao Chu] D. Bandyopadhyay

More information

ECLT 5810 Linear Regression and Logistic Regression for Classification. Prof. Wai Lam

ECLT 5810 Linear Regression and Logistic Regression for Classification. Prof. Wai Lam ECLT 5810 Linear Regression and Logistic Regression for Classification Prof. Wai Lam Linear Regression Models Least Squares Input vectors is an attribute / feature / predictor (independent variable) The

More information

7.1, 7.3, 7.4. Timothy Hanson. Department of Statistics, University of South Carolina. Stat 770: Categorical Data Analysis 1/ 31

7.1, 7.3, 7.4. Timothy Hanson. Department of Statistics, University of South Carolina. Stat 770: Categorical Data Analysis 1/ 31 7.1, 7.3, 7.4 Timothy Hanson Department of Statistics, University of South Carolina Stat 770: Categorical Data Analysis 1/ 31 7.1 Alternative links in binary regression* There are three common links considered

More information

Correlated data. Non-normal outcomes. Reminder on binary data. Non-normal data. Faculty of Health Sciences. Non-normal outcomes

Correlated data. Non-normal outcomes. Reminder on binary data. Non-normal data. Faculty of Health Sciences. Non-normal outcomes Faculty of Health Sciences Non-normal outcomes Correlated data Non-normal outcomes Lene Theil Skovgaard December 5, 2014 Generalized linear models Generalized linear mixed models Population average models

More information

Lecture 3.1 Basic Logistic LDA

Lecture 3.1 Basic Logistic LDA y Lecture.1 Basic Logistic LDA 0.2.4.6.8 1 Outline Quick Refresher on Ordinary Logistic Regression and Stata Women s employment example Cross-Over Trial LDA Example -100-50 0 50 100 -- Longitudinal Data

More information

Exercise 5.4 Solution

Exercise 5.4 Solution Exercise 5.4 Solution Niels Richard Hansen University of Copenhagen May 7, 2010 1 5.4(a) > leukemia

More information

ij i j m ij n ij m ij n i j Suppose we denote the row variable by X and the column variable by Y ; We can then re-write the above expression as

ij i j m ij n ij m ij n i j Suppose we denote the row variable by X and the column variable by Y ; We can then re-write the above expression as page1 Loglinear Models Loglinear models are a way to describe association and interaction patterns among categorical variables. They are commonly used to model cell counts in contingency tables. These

More information

Epidemiology Wonders of Biostatistics Chapter 11 (continued) - probability in a single population. John Koval

Epidemiology Wonders of Biostatistics Chapter 11 (continued) - probability in a single population. John Koval Epidemiology 9509 Wonders of Biostatistics Chapter 11 (continued) - probability in a single population John Koval Department of Epidemiology and Biostatistics University of Western Ontario What is being

More information

Logistic Regression. Building, Interpreting and Assessing the Goodness-of-fit for a logistic regression model

Logistic Regression. Building, Interpreting and Assessing the Goodness-of-fit for a logistic regression model Logistic Regression In previous lectures, we have seen how to use linear regression analysis when the outcome/response/dependent variable is measured on a continuous scale. In this lecture, we will assume

More information

n y π y (1 π) n y +ylogπ +(n y)log(1 π).

n y π y (1 π) n y +ylogπ +(n y)log(1 π). Tests for a binomial probability π Let Y bin(n,π). The likelihood is L(π) = n y π y (1 π) n y and the log-likelihood is L(π) = log n y +ylogπ +(n y)log(1 π). So L (π) = y π n y 1 π. 1 Solving for π gives

More information

STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis. 1. Indicate whether each of the following is true (T) or false (F).

STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis. 1. Indicate whether each of the following is true (T) or false (F). STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis 1. Indicate whether each of the following is true (T) or false (F). (a) (b) (c) (d) (e) In 2 2 tables, statistical independence is equivalent

More information

4.5.1 The use of 2 log Λ when θ is scalar

4.5.1 The use of 2 log Λ when θ is scalar 4.5. ASYMPTOTIC FORM OF THE G.L.R.T. 97 4.5.1 The use of 2 log Λ when θ is scalar Suppose we wish to test the hypothesis NH : θ = θ where θ is a given value against the alternative AH : θ θ on the basis

More information

Review of One-way Tables and SAS

Review of One-way Tables and SAS Stat 504, Lecture 7 1 Review of One-way Tables and SAS In-class exercises: Ex1, Ex2, and Ex3 from http://v8doc.sas.com/sashtml/proc/z0146708.htm To calculate p-value for a X 2 or G 2 in SAS: http://v8doc.sas.com/sashtml/lgref/z0245929.htmz0845409

More information

Lecture 8: Summary Measures

Lecture 8: Summary Measures Lecture 8: Summary Measures Dipankar Bandyopadhyay, Ph.D. BMTRY 711: Analysis of Categorical Data Spring 2011 Division of Biostatistics and Epidemiology Medical University of South Carolina Lecture 8:

More information

NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION (SOLUTIONS) ST3241 Categorical Data Analysis. (Semester II: )

NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION (SOLUTIONS) ST3241 Categorical Data Analysis. (Semester II: ) NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION (SOLUTIONS) Categorical Data Analysis (Semester II: 2010 2011) April/May, 2011 Time Allowed : 2 Hours Matriculation No: Seat No: Grade Table Question 1 2 3

More information

MULTINOMIAL LOGISTIC REGRESSION

MULTINOMIAL LOGISTIC REGRESSION MULTINOMIAL LOGISTIC REGRESSION Model graphically: Variable Y is a dependent variable, variables X, Z, W are called regressors. Multinomial logistic regression is a generalization of the binary logistic

More information

Models for Ordinal Response Data

Models for Ordinal Response Data Models for Ordinal Response Data Robin High Department of Biostatistics Center for Public Health University of Nebraska Medical Center Omaha, Nebraska Recommendations Analyze numerical data with a statistical

More information

Arijit Das Center for Economic Studies and Planning Jawaharlal Nehru University

Arijit Das Center for Economic Studies and Planning Jawaharlal Nehru University Arijit Das Center for Economic Studies and Planning Jawaharlal Nehru University A large number of case studies on collective action in Common property resources. Absence of universal model to identify

More information

Good Confidence Intervals for Categorical Data Analyses. Alan Agresti

Good Confidence Intervals for Categorical Data Analyses. Alan Agresti Good Confidence Intervals for Categorical Data Analyses Alan Agresti Department of Statistics, University of Florida visiting Statistics Department, Harvard University LSHTM, July 22, 2011 p. 1/36 Outline

More information

EDF 7405 Advanced Quantitative Methods in Educational Research. Data are available on IQ of the child and seven potential predictors.

EDF 7405 Advanced Quantitative Methods in Educational Research. Data are available on IQ of the child and seven potential predictors. EDF 7405 Advanced Quantitative Methods in Educational Research Data are available on IQ of the child and seven potential predictors. Four are medical variables available at the birth of the child: Birthweight

More information

11 November 2011 Department of Biostatistics, University of Copengen. 9:15 10:00 Recap of case-control studies. Frequency-matched studies.

11 November 2011 Department of Biostatistics, University of Copengen. 9:15 10:00 Recap of case-control studies. Frequency-matched studies. Matched and nested case-control studies Bendix Carstensen Steno Diabetes Center, Gentofte, Denmark http://staff.pubhealth.ku.dk/~bxc/ Department of Biostatistics, University of Copengen 11 November 2011

More information

Categorical data analysis Chapter 5

Categorical data analysis Chapter 5 Categorical data analysis Chapter 5 Interpreting parameters in logistic regression The sign of β determines whether π(x) is increasing or decreasing as x increases. The rate of climb or descent increases

More information

" M A #M B. Standard deviation of the population (Greek lowercase letter sigma) σ 2

 M A #M B. Standard deviation of the population (Greek lowercase letter sigma) σ 2 Notation and Equations for Final Exam Symbol Definition X The variable we measure in a scientific study n The size of the sample N The size of the population M The mean of the sample µ The mean of the

More information