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


 Logan Garrett
 2 years ago
 Views:
Transcription
1 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 binary response variables Similar in intent to linear regression, but details are different Method for estimating joint association between several predictors and a response variable Typically useful in some class projects 1
2 2
3 Betting in a fair game An American roulette wheel has 38 slots: 1,2,3,, 36, 0, 00 If you place a $1 bet on 00 for a single spin of the wheel, you have 1/38 chance of winning in a single spin 1 way to win, 37 ways to lose, or The casino has 37 ways to win, 1 way to lose The odds of winning for the house are 37 to 1, 1 to 37 for you 3
4 Betting in roulette... For the game to be fair, Casino keeps your $1 if 00 does not come up Casino pays $37 if 00 comes up, and you keep your bet If X is your winnings from a $1 bet, E(X) = 1 (37/38) + 37 (1/38) = 0 Casinos stay in business by paying out 35 to 1, the casinos insure that roulette is not a fair game. In this case E(X) = 1 (37/38) + 35 (1/38) = (2/38) =
5 Converting probabilities to odds and log(odds) In a game of chance, the odds of winning is the same as the ratio of money that should be bet by the two players. In roulette, the odds of your winning is the ratio of the probability of your winning to the probability of losing p/(1p) = (1/38) / (37/38) = 1/37 Typically, odds are given to show the ratio of the payout: 37 to 1 in this case The values of an `odds range from 0 to Think of probabilities 0.01, 0.001, , 0.99, 0.999, ,etc We will use a transformation of odds to log(odds) The values of log(odds) range from  to. 5
6 Odds vs log(odds) Transformation of p Why consider such a transformation? Answer: it transforms a 0 < p < 1 variable to a quantitative variable from  to + It is a simple algebraic operation to go back and forth between probabilities and log(odds) Odds Log odds p p/(1p) log(p/(1p))
7 Computing odds in data, an example The example on the next slide is very similar to IPS Example 8.1 (5th and 6th edition), but the numbers are from the 5th ed. Be careful when reading the example in the 6th ed. 7
8 Example: binge drinking survey Binger Men Women Total Yes % % 3314 No % Total % % %
9 Logistic Regression Idea behind logistic regression Let ˆp M be the proportion of men who are binge drinkers; log(ˆp M /(1 ˆp M )) is the log odds. Let ˆp F be the proportion of women who are binge drinkers; log(ˆp F /(1 ˆp F )) is the log odds. The ratio of the odds (called the odds ratio) of men to women being binge drinkers is ˆp M 1 ˆp M = ˆp F 1 ˆp F ( ˆpM )( 1 ˆpF 1 ˆp M ˆp F ) = = Now recall log(x/y) = log(x) log(y). 9
10 New page Idea behind logistic regression In the binge drinking table, log [( ˆpM )( 1 ˆpF 1 ˆp M ˆp F )] = log(0.294) log(0.205) = ( 1.587) = The log odds for males differs from the log odds for females by a constant. Logistic regresson is a model in which predictors induce changes in log(odds), similar to linear regression, where Predictors induce changes in mean of response variable. 10
11 Model for Logistic Regression Set the log odds to be a linear combination of the predictor variables This is the Logistic Regression Model Sometimes equivalently written as: 11
12 Logistic regression The Logistic Regression Model Predictor variables (x s) can be quantitative or binary More complex formulas for estimates than least squares Omnibus test of the model now a χ 2, not an F test We can test each predictor variable (x i ) for its contribution but now this is a z test, not a t test Assumptions of this model are quite complex and are not often checked Logistic regression model is widely used Coefficients can be derived directly in some 2way tables Back to binge drinking example 12
13 Example: binge drinking survey Binger Men Women Total Yes % % % No % Total % % % % % 13
14 The logistic model  binge drinking From the previous slide (odds of being a binge drinker) For men: Log odds = For women: Log odds = The logistic model for one predictor (gender) is Log (p /(1p)) = Log odds = b0 + b1x1 where Y = 1 if a binge drinker; 0 otherwise and X1 = 1 if male; 0 if female So the logistic model is For men: Log odds = b0 + b1 = For women: Log odds = b0 = Solving b0 = and b1 = b0 = Thus the fitted logistic model for this example is Log odds = X1 14
15 The logistic model  binge drinking Working backwards to confirm this fitted model Log odds = log (p/(1p)) = X 1 where X 1 = 1 if male and X 1 = 0 if female So for men Log odds = log (p/(1p)) = (1) = and odds = e = Thus the proportion of binge drinkers is odds / (odds +1) = / = For women Log odds = log (p/(1p)) = and odds = e = Thus the proportion of binge drinkers is odds / (odds +1) = / =
16 Comparing two proportions Relative risk and odds ratio S F Total Group 1 a b a + b Group 2 c d c + d Total a + c b + d 16
17 Odds ratio As with RR, an odds ratio of 1 indicates the proportion of successes (events) is the same in both groups RR is easier to interpret (ratio of sample proportions) When successes are rare, RR and OR are very similar When successes are common, RR and OR are similar only if they are close to 1 OR tends to overstate differences Example: binge drinking 17
18 Odds ratio and logistic regression Odds ratio is the key output from a logistic regression An OR is calculated for each predictor variable OR measures the strength of the effect on p (probability of `success ) Example: binge drinking Log odds = X 1 where X 1 = 1 if M, 0 if F For men: Log odds = b 0 + b 1 = For women: Log odds = b 0 = Let OR be the odds ratio men to women Log (OR) = log (odds for men) log (odds for women) = (b 0 + b 1 ) (b 0 ) = b 1 So OR = e b 1 For the binge drinking example OR = e =
19 Inference for logistic regression parameters A 95% confidence interval for the coefficient β 1 is given by b 1 ± 1.96 s.e.(b 1 ) A 95% confidence interval for the odds ratio e β 1 is given by e (b 1± 1.96 s.e.(b 1 )) To test the null hypothesis H 0 : β 1 =0(i.e., no association between the response variable and the predictor variable X 1 ), use Z = b 1 s.e.(b 1 ) Z has (approximately) a N(0, 1) distribution when H 0 is true. 19
20 Binge drinking: expanding data from a 2x2 table to a rectangular data file The 2x2 table Let Binge = 1 if binger Let Sex = 1 if male 0 otherwise Stata commands input Binge Sex Count end expand Count Binger Men Women Total Yes No Total This creates a rectangular data file with 17,096 rows: etc. 20
21 Binge drinking logistic regression Stata has 2 commands  logistic and logit logistic displays ORs; logit displays model coefficients Note: b 0 = and b 1 = as earlier 21
22 Binge drinking logistic regression Logistic command displays the odds ratio Notes: OR = as earlier 95% CI for OR (1.33, 1.55) excludes OR = 1 z for the Wald test = 9.31 (P < 0.001) 22
23 Multiple logistic regression Example: Intensive Care Unit (ICU) Study of 200 patients admitted to the adult ICU at Baystate Medical Center in Springfield, MA Response variable Survival until hospital discharge (Surv) Surv = 1 if died, 0 if survived Predictor variables Age, in years (Age) Sex = 1 if female, 0 if male (Sex) Race = 1 if white, 0 otherwise (Race) Heart rate at ICU admission, beats/min. (HRate) Level of consciousness at ICU admission (LOC) LOC = 1 if deep stupor of coma, 0 otherwise Source: Hosmer & Lemeshow (2000) Wiley & Sons 23
24 Density Heart Rate at ICU Admission Density Age Density 0 Density Age Heart Rate at ICU Admission 200. table LOC Level of Consciousness at ICU Admission Freq. No Coma or Deep Stupor 185 Deep Stupor 5 Coma 10. table surv surv Freq
25 Example ICU, summary of the data Response variable  survival to hospital discharge Surv N = 200, 20% died Predictor variables Sex 38% female Age Average is 57.5 yrs., range from 16 to 92 yrs. Race 87.5% white HRate Average is 99, range from 39 to 192 beats/min. LOC 7.5% in deep stupor or coma 25
26 ICU  predictors of death before discharge A logistic regression with all 5 predictors Age and level of consciousness (LOC) both significant Reestimate the model keeping only the significant terms 26
27 ICU  predictors of death before discharge The final logistic model (using logistic command) Age and LOC are significant Odds ratio For Age (95% CI is to 1.064) P = For LOC (95% CI is 7.63 to ) P <
28 ICU  predictors of death before discharge The final logistic model (using logit command) Shows the logistic model coefficients Log odds = Log (p/1p) = Age LOC Note: e = (OR) and e 3.59 = (OR for LOC) 28
29 Interpretation of coefficients of the logistic regression model The sign of the β i term indicates whether p increases or decreases as x increases ICU Example: both β i terms were positive so risk of death increases with age and presence of deep stupor or coma The magnitude of the β i term gives the additive change in log odds when there is +1 unit change in the predictor variable, holding other predictors fixed 29
30 Interpretation of coefficients The magnitude of the odds ratio term (= e βi ) gives the multiplicative change in odds for +1 change in predictor ICU Example: the odds of death increases multiplicatively by 2.8% (OR = 1.028) for each year increase in age To see this, exponentiate both sides of logistic model and note (p/1p) = e β0 + β1[x + 1] = (e β0 )(e β1x )(e β1 ), where e β1 = OR 30
31 Final Thoughts on Logistic Regression Some of you will find logistic regression useful in a project, so last pset has logistic regression problem. Not covered on final exam, because we have not had time to digest it. Logistic regression extends the analysis of twoway tables Response variable must still be binary. Predictors can now be categorical or quantitative. Logistic regression is an example of a class of regression models much more general than linear regression. These models are covered in detail in Stat 138 and Stat
11. 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 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 informationExpected Value. 24 February 2014. Expected Value 24 February 2014 1/19
Expected Value 24 February 2014 Expected Value 24 February 2014 1/19 This week we discuss the notion of expected value and how it applies to probability situations, including the various New Mexico Lottery
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 informationVI. 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 informationImproved Interaction Interpretation: Application of the EFFECTPLOT statement and other useful features in PROC LOGISTIC
Paper AA082013 Improved Interaction Interpretation: Application of the EFFECTPLOT statement and other useful features in PROC LOGISTIC Robert G. Downer, Grand Valley State University, Allendale, MI ABSTRACT
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 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 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 informationTHE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/
THE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/ Is it possible to earn money from online gambling? Are there any 100% sure winning roulette systems? Are there actually people who make a living
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 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 informationMath 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2
Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable
More informationHYPOTHESIS TESTING: CONFIDENCE INTERVALS, TTESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, TTESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
More informationThe first three steps in a logistic regression analysis with examples in IBM SPSS. Steve Simon P.Mean Consulting www.pmean.com
The first three steps in a logistic regression analysis with examples in IBM SPSS. Steve Simon P.Mean Consulting www.pmean.com 2. Why do I offer this webinar for free? I offer free statistics webinars
More informationFinding Supporters. Political Predictive Analytics Using Logistic Regression. Multivariate Solutions
Finding Supporters Political Predictive Analytics Using Logistic Regression Multivariate Solutions What is Logistic Regression? In a political application, logistic regression can describe the outcome
More informationGeneral Method: Difference of Means. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n
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 informationIf, under a given assumption, the of a particular observed is extremely. , we conclude that the is probably not
4.1 REVIEW AND PREVIEW RARE EVENT RULE FOR INFERENTIAL STATISTICS If, under a given assumption, the of a particular observed is extremely, we conclude that the is probably not. 4.2 BASIC CONCEPTS OF PROBABILITY
More informationSolutions: Problems for Chapter 3. Solutions: Problems for Chapter 3
Problem A: You are dealt five cards from a standard deck. Are you more likely to be dealt two pairs or three of a kind? experiment: choose 5 cards at random from a standard deck Ω = {5combinations of
More informationIII. 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 informationInternational Statistical Institute, 56th Session, 2007: Phil Everson
Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA Email: peverso1@swarthmore.edu 1. Introduction
More informationStatistics 151 Practice Midterm 1 Mike Kowalski
Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and
More information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
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 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 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 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 informationStudents' Opinion about Universities: The Faculty of Economics and Political Science (Case Study)
Cairo University Faculty of Economics and Political Science Statistics Department English Section Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study) Prepared
More informationSurvival 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 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 informationIs it statistically significant? The chisquare test
UAS Conference Series 2013/14 Is it statistically significant? The chisquare test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chisquare? Tests whether two categorical
More informationLogistic Regression. BUS 735: Business Decision Making and Research
Goals of this section 2/ 8 Specific goals: Learn how to conduct regression analysis with a dummy independent variable. Learning objectives: LO2: Be able to construct and use multiple regression models
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 informationTesting on proportions
Testing on proportions Textbook Section 5.4 April 7, 2011 Example 1. X 1,, X n Bernolli(p). Wish to test H 0 : p p 0 H 1 : p > p 0 (1) Consider a related problem The likelihood ratio test is where c is
More informationChi Squared and Fisher's Exact Tests. Observed vs Expected Distributions
BMS 617 Statistical Techniques for the Biomedical Sciences Lecture 11: ChiSquared and Fisher's Exact Tests Chi Squared and Fisher's Exact Tests This lecture presents two similarly structured tests, Chisquared
More informationElementary Statistics and Inference. Elementary Statistics and Inference. 17 Expected Value and Standard Error. 22S:025 or 7P:025.
Elementary Statistics and Inference S:05 or 7P:05 Lecture Elementary Statistics and Inference S:05 or 7P:05 Chapter 7 A. The Expected Value In a chance process (probability experiment) the outcomes of
More informationYou can place bets on the Roulette table until the dealer announces, No more bets.
Roulette Roulette is one of the oldest and most famous casino games. Every Roulette table has its own set of distinctive chips that can only be used at that particular table. These chips are purchased
More informationAuxiliary Variables in Mixture Modeling: 3Step Approaches Using Mplus
Auxiliary Variables in Mixture Modeling: 3Step 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 informationMultiple logistic regression analysis of cigarette use among high school students
Multiple logistic regression analysis of cigarette use among high school students ABSTRACT Joseph AdwereBoamah Alliant International University A binary logistic regression analysis was performed to predict
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 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 information1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ
STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material
More informationCurriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
More informationLesson 14 14 Outline Outline
Lesson 14 Confidence Intervals of Odds Ratio and Relative Risk Lesson 14 Outline Lesson 14 covers Confidence Interval of an Odds Ratio Review of Odds Ratio Sampling distribution of OR on natural log scale
More informationX X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)
CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.
More informationSection Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini
NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building
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 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 informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationRaul CruzCano, HLTH653 Spring 2013
Multilevel ModelingLogistic Schedule 3/18/2013 = Spring Break 3/25/2013 = Longitudinal Analysis 4/1/2013 = Midterm (Exercises 15, not Longitudinal) Introduction Just as with linear regression, logistic
More informationStatistics 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 informationElementary Statistics
Elementary Statistics Chapter 1 Dr. Ghamsary Page 1 Elementary Statistics M. Ghamsary, Ph.D. Chap 01 1 Elementary Statistics Chapter 1 Dr. Ghamsary Page 2 Statistics: Statistics is the science of collecting,
More informationAdvanced Quantitative Methods for Health Care Professionals PUBH 742 Spring 2015
1 Advanced Quantitative Methods for Health Care Professionals PUBH 742 Spring 2015 Instructor: Joanne M. Garrett, PhD email: joanne_garrett@med.unc.edu Class Notes: Copies of the class lecture slides
More informationANALYSING 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 informationElementary Statistics
lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chisquare Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page
More informationInteraction between quantitative predictors
Interaction between quantitative predictors In a firstorder model like the ones we have discussed, the association between E(y) and a predictor x j does not depend on the value of the other predictors
More informationIntroduction to Stata
Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the midrange of how easy it is to use. Other options include SPSS,
More informationSimple Linear Regression
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
More informationThe point estimate you choose depends on the nature of the outcome of interest odds ratio hazard ratio
Point Estimation Definition: A point estimate is a onenumber summary of data. If you had just one number to summarize the inference from your study.. Examples: Dose finding trials: MTD (maximum tolerable
More informationMind on Statistics. Chapter 15
Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,
More informationIntroduction to Analysis Methods for Longitudinal/Clustered Data, Part 3: Generalized Estimating Equations
Introduction to Analysis Methods for Longitudinal/Clustered Data, Part 3: Generalized Estimating Equations Mark A. Weaver, PhD Family Health International Office of AIDS Research, NIH ICSSC, FHI Goa, India,
More informationIn the situations that we will encounter, we may generally calculate the probability of an event
What does it mean for something to be random? An event is called random if the process which produces the outcome is sufficiently complicated that we are unable to predict the precise result and are instead
More informationUse of the ChiSquare Statistic. Marie DienerWest, PhD Johns Hopkins University
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 informationMA 1125 Lecture 14  Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.
MA 5 Lecture 4  Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
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 informationAdvanced Statistical Analysis of Mortality. Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc. 160 University Avenue. Westwood, MA 02090
Advanced Statistical Analysis of Mortality Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc 160 University Avenue Westwood, MA 02090 001(781)7516356 fax 001(781)3293379 trhodes@mib.com Abstract
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 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 informationIf You Think Investing is Gambling, You re Doing it Wrong!
If You Think Investing is Gambling, You re Doing it Wrong! Warren Buffet Jennifer Arthur, M.Sc. PhD Candidate, University of Adelaide Supervisor: Dr. Paul Delfabbro 10th European Conference on Gambling
More informationBRIEF OVERVIEW ON INTERPRETING COUNT MODEL RISK RATIOS
BRIEF OVERVIEW ON INTERPRETING COUNT MODEL RISK RATIOS An Addendum to Negative Binomial Regression Cambridge University Press (2007) Joseph M. Hilbe 2008, All Rights Reserved This short monograph is intended
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 5.1 Homework Answers 5.7 In the proofreading setting if Exercise 5.3, what is the smallest number of misses m with P(X m)
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
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 informationThe Math. P (x) = 5! = 1 2 3 4 5 = 120.
The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct
More informationMath 108 Exam 3 Solutions Spring 00
Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8
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 informationChapter 23. Inferences for Regression
Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily
More informationNominal and ordinal logistic regression
Nominal and ordinal logistic regression April 26 Nominal and ordinal logistic regression Our goal for today is to briefly go over ways to extend the logistic regression model to the case where the outcome
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 informationChapter 7: Proportional Play and the Kelly Betting System
Chapter 7: Proportional Play and the Kelly Betting System Proportional Play and Kelly s criterion: Investing in the stock market is, in effect, making a series of bets. Contrary to bets in a casino though,
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 informationSection 7C: The Law of Large Numbers
Section 7C: The Law of Large Numbers Example. You flip a coin 00 times. Suppose the coin is fair. How many times would you expect to get heads? tails? One would expect a fair coin to come up heads half
More informationMONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010
MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times
More informationIntroduction. Hypothesis Testing. Hypothesis Testing. Significance Testing
Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters
More informationStatistics in Medicine Research Lecture Series CSMC Fall 2014
Catherine Bresee, MS Senior Biostatistician Biostatistics & Bioinformatics Research Institute Statistics in Medicine Research Lecture Series CSMC Fall 2014 Overview Review concept of statistical power
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 informationModule 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 informationIrfan Syed, M.B.B.S., M.P.H Sandra Minor Bulmer, Ph.D. Christine Unson, Ph.D.
Determinants and Correlations of Excessive Alcohol Use and Depression among College Students in a North East University Irfan Syed, M.B.B.S., M.P.H Sandra Minor Bulmer, Ph.D. Christine Unson, Ph.D. SOUTHERN
More informationAnalysis of Survey Data Using the SAS SURVEY Procedures: A Primer
Analysis of Survey Data Using the SAS SURVEY Procedures: A Primer Patricia A. Berglund, Institute for Social Research  University of Michigan Wisconsin and Illinois SAS User s Group June 25, 2014 1 Overview
More informationExample. A casino offers the following bets (the fairest bets in the casino!) 1 You get $0 (i.e., you can walk away)
: Three bets Math 45 Introduction to Probability Lecture 5 Kenneth Harris aharri@umich.edu Department of Mathematics University of Michigan February, 009. A casino offers the following bets (the fairest
More informationCalculating the Probability of Returning a Loan with Binary Probability Models
Calculating the Probability of Returning a Loan with Binary Probability Models Associate Professor PhD Julian VASILEV (email: vasilev@uevarna.bg) Varna University of Economics, Bulgaria ABSTRACT The
More informationSchool of Nursing Faculty Salary Equity Report and Action Plan
July 1, 2015 School of Nursing Faculty Salary Equity Report and Action Plan Shari L. Dworkin, Ph.D., M.S. Associate Dean for Academic Affairs Overview: In 2012, then UC President Mark Yudof charged each
More informationOutline. Dispersion Bush lupine survival QuasiBinomial family
Outline 1 Threeway interactions 2 Overdispersion in logistic regression Dispersion Bush lupine survival QuasiBinomial family 3 Simulation for inference Why simulations Testing model fit: simulating the
More information" 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 informationEstimation of σ 2, the variance of ɛ
Estimation of σ 2, the variance of ɛ The variance of the errors σ 2 indicates how much observations deviate from the fitted surface. If σ 2 is small, parameters β 0, β 1,..., β k will be reliably estimated
More informationChapter 7: Dummy variable regression
Chapter 7: Dummy variable regression Why include a qualitative independent variable?........................................ 2 Simplest model 3 Simplest case.............................................................
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 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 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 information