Stat 642, Lecture notes for 04/12/05 96


 Gervais Gregory
 1 years ago
 Views:
Transcription
1 Stat 642, Lecture notes for 04/12/05 96 HosmerLemeshow Statistic The HosmerLemeshow Statistic is another measure of lack of fit. Hosmer and Lemeshow recommend partitioning the observations into 10 equal sized groups according to their predicted probabilities. Then where G 2 HL = 10 j=1 O j E j 2 E j 1 E j /n j χ2 8 n j = Number of observations in the j th group O j = i E j = i y ij = Observed number of cases in the j th group ˆp ij = Expected number of cases in the j th group Example: Using the THS data described earlier 4/7/2005, I added the lackfit option to the model statement in PROC LOGISTIC as follows: model cens28dy = trt age sbpcat aist hctbase / lackfit; The output corresponding to the HosmerLemeshow statistic is: Partition for the Hosmer and Lemeshow Test CENS28DY = 0 CENS28DY = 1 Group Total Observed Expected Observed Expected Hosmer and Lemeshow GoodnessofFit Test ChiSquare DF Pr > ChiSq
2 Stat 642, Lecture notes for 04/12/05 97 This output shows the observed and expected numbers of cases and controls within each group, and the final test statistic. The chisquare statistic suggests that there may be lack of fit, so I refit the model including a quadratic term for age: model cens28dy = trt age age sbpcat aist hctbase / lackfit; Partition for the Hosmer and Lemeshow Test CENS28DY = 0 CENS28DY = 1 Group Total Observed Expected Observed Expected Hosmer and Lemeshow GoodnessofFit Test ChiSquare DF Pr > ChiSq This model shows no evidence of lack of fit based on the HL statistic, so apparently any lack of fit has been corrected. Ideally, incorrect model specification such as nonlinearity in the predictors or missing predictors should be detectable by this statistic. However, depending on the model, G 2 LH may not be particularly sensitive to departures from the true model. The HL test does not provide any information regarding the nature of the lack of fit observed. Other procedures may be more useful. Other goodnessoffit procedures Tsiatis A note on the goodnessoffit test for the istic regression model, Biometrika, 67: , 1980 proposes a test for goodnessoffit obtained by grouping observations into k groups according to covariate values. The goodnessoffit test uses the score test of H 0 that the fitted model is correct, versus the model which adds to the fitted model a categorical variable corresponding to the groupings. For example, for the model above, one could group observations by age categories possibly equally spaced, or of equal size  the groups are somewhat arbitrary, and perform the score test for the addition of these groupings to the model similar to what one would do in a forward selection procedure.
3 Stat 642, Lecture notes for 04/12/05 98 Lin, Wei and Ying Model checking techniques based on cumulative residuals, Biometrics, 58:112, 2002 propose assessing goodnessoffit using moving sums of residuals of the form: W x = i Ix b < X ij < x + by i Ey i where I is one if the argument is true, and zero otherwise, x is an arbitrary value of covariate j and X ij is the value of covariate j for subject i. W x is simply the total observed  expected for all observations with the value covariate j within b units of x. By plotting W x against x for values of x over the range of the covariate, patterns may be apparent which suggest lack of fit. LWY propose a formal test using simulation to assess whether the observed patterns are likely by chance alone. The score test of Tsiatis may also be used to provide a formal test. Polychotomous Responses note that in the interest of time, I skipped over some of the material in this section during class Now we consider the case in which we have more than two levels of outcome variable. Examples Type of Disease Site of Onset e.g. tumor Disease Severity ordered Cause of Death Suppose that we have k + 1 response categories, 0, 1,..., k. Under a multinomial model there are k + 1 event probabilities which sum to one. Hence there are k independent its to model. We consider three approaches to this modeling, all of which produce different results. Loglinear model Continuation Ratios Cumulative Logit Loglinear Model Poisson Sampling model Suppose we have a covariate with levels 0, 1, 2,.... We may construct the following table:
4 Stat 642, Lecture notes for 04/12/05 99 Response k Covariate Values For the i, j cell, we have the linear model λ ij = α i + β j + γ ij where we impose the constraint that γ 0j = γ i0 = 0 i, j. We could, for example, choose a baseline category for the response, say i = 0. Then λij λ 0j = pij p 0j = α i α 0 + γ ij Then γ ij is the odds ratio for response level i versus level 0 and exposure level j versus level 0. This may be called the baseline it model. Similarly, if the responses are naturally ordered, then it may be reasonable to consider adjacent categories: λi+1,j λ i,j = pi+1,j p i,j = α i+1 α i + γ i+1,j γ i,j = α i + γ i,j Then γij is the odds ratio for response level i + 1 versus level i and exposure level j versus level 0. More generally, we might have In which case pij p 0j λ ij = x T j β i We may compute the probabilities themselves via = x T j β i β 0 = x T j β i. p ij = e x jβ i 1 + l 1 ex jβ l For example, if k = 2, we have: p 0j = e x jβ1 + e x jβ2, p 1j = e x jβ e x jβ 1 + e x jβ 2 p 2j = e x jβ e x jβ 1 + e x jβ 2 Hypothetical example: Suppose we consider death from Heart Disease or Cancer. There is no particular order to these outcomes, so this kind of model may make some sense. In the accompanying
5 Stat 642, Lecture notes for 04/12/ plot, the probabilities of death from heart disease and cancer change as a function of age and this model allows them to change quite independently. Hypothetical Example Death from Heart Disease vs. Cancer Heart Disease Cancer Survival or Other Probability Age Note that if we consider a plot of its for each of heart disease and cancer versus survival we have straight lines: Hypothetical Example  it scale Heart Disease Cancer p i /p 0 Age
6 Stat 642, Lecture notes for 04/12/ Continuation Ratios Take k = 2 for a moment and consider two parallel schemes for constructing the 2 independent its: In General: Scheme A p0j p 1j + p 2j p1j p 2j pij l>i p lj Scheme B p2j p 0j + p 1j p1j p 0j pij l<i p lj If the categories are 0, 1, 2,..., k, then under Scheme A, we first consider the lowest category i = 0 versus all remaining categories. For each category i, i < k, we consider category i versus all higher categories. Under Scheme B, we consider for each category i, i < 0, we consider category i versus all lower categories. For example, if the categories are Alive, Heart Disease Death and Cancer Death, we might consider its for Alive versus Dead and among the deaths Heart Disease Death versus Cancer Death. If we set the i th it equal to x T j β i, we can express the multinomial probabilities of being in a particular category as follows: take k = 3, Scheme A. First we have that next, Similarly, Finally, p 0j = Pr{y j = 0} = ext β e xt β 0 p 1j = Pr{y j = 1} = Pr{y j = 1 y j 1} Pr{y j 1} = e xt β e xt β e xt β 0. p 2j = Pr{y j = 2} = Pr{y j = 2 y j 2} Pr{y j 2 y j 1} Pr{y j 1} = e xt β e xt β e xt β e xt β 0 p 3j = Pr{y j = 3} = Pr{y j = 3 y j 2} Pr{y j 2 y j 1} Pr{y j 1} = e xt β e xt β e xt β 0
7 Stat 642, Lecture notes for 04/12/ In all cases, the p ij are products of conditional probabilities each of which depends one only on one of the β i. Since the likelihood is composed of products of the above p ij, it will also factor into a product of conditional likelihoods, each of which can be independently maximized. Hence, this model can be fit as a series of binary istic regression models. Each binary model is fit by restricting the data set to only those observations with responses in categories i through k under Scheme A or 0 through i under Scheme B and considering response level i versus the remaining categories. Continuation Ratio models give different fitted values than linear models and Scheme A gives different fitted values than Scheme B. Cumulative Logits. Cumulative Logit models are typically used when we have ordinal responses. That is, we may consider the outcomes as a series of progressively worse or more extreme outcomes. In this case the relevant questions usually involve probabilities of subjects progressing from one category to the next, or probabilities of a subject being above of a given category versus at or lower than a given category. Example: Disease Severity Percent of Subjects None Mild Moderate Severe  + Exposure In the above plot, the size of the none category decreases slightly with exposure. This suggests that exposure increases the risk of disease without regard for severity. On the other hand, the mild category also decreases with exposure, yet this fact by itself is not very meaningful since we don t know whether or not subjects who otherwise would have been in the mild category were moved to the none category or the moderate or worse categories. The conclusion might be quite different depending on which of these happened. More meaningful is the observation that
8 Stat 642, Lecture notes for 04/12/ the combined none and mild categories shrunk, suggesting that the rate of moderate or worse disease increased. This leads us to the cumulative it model: Pr{yj i} = α i + x T j Pr{y j > i} β i. If β i = β i, this is the Proportional Odds model. We also require that α 0 α 1... although this will hold automatically in a proportional odds model. eα i+x T j β i We have Pr{y j i} =. 1 + e α i+x T j β i Note that if β i β i for some i i, then α i + β i x = α i + β i x for some x and the lines will cross. If α i + x T j β i > α i + x T j β i for some i < i then Pr{y j i} > Pr{y j i } which is nonsense. Hence if a cumulative it model is NOT a proportional odds model, there may be particular values of x for which the predicted values are inconsistent. Under the proportional odds model, the shapes of all curves are the same, they are shifted progressively to the left for increasing i. The horizontal distance between adjacent curves is α i α i 1 /β. Pr{y i} i = 0 i = 1 i = 2 Pr{y = 3 x} Pr{y = 2 x} Pr{y = 1 x} Pr{y = 0 x} Odds Ratios: Let the odds of {y j i} be ψ ij = Pr{y j i} Pr{y j > i} = eα i+x T j β x so and ψ ij ψ i j ψ ij ψ ij = e α i α i is independent of j proportional odds = e x j x j T β is independent of i With more than two levels of the outcome variable, SAS fits a proportional odds model and uses the score test for to test for proportionality.
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 informationLogistic Regression. Interpretation of linear regression. Other types of outcomes. 01 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 informationChapter 5: Logistic RegressionI
: Logistic RegressionI Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM [Acknowledgements to Tim Hanson and Haitao Chu] D. Bandyopadhyay
More information8 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 informationLongitudinal 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 informationCorrelation and regression
1 Correlation and regression Yongjua Laosiritaworn Introductory on Field Epidemiology 6 July 2015, Thailand Data 2 Illustrative data (Doll, 1955) 3 Scatter plot 4 Doll, 1955 5 6 Correlation coefficient,
More informationSTA6938Logistic Regression Model
Dr. Ying Zhang STA6938Logistic Regression Model Topic 2Multiple Logistic Regression Model Outlines:. Model Fitting 2. Statistical Inference for Multiple Logistic Regression Model 3. Interpretation of
More informationAnalysing categorical data using logit models
Analysing categorical data using logit models Graeme Hutcheson, University of Manchester The lecture notes, exercises and data sets associated with this course are available for download from: www.researchtraining.net/manchester
More informationGeneralized Linear Modeling  Logistic Regression
1 Generalized Linear Modeling  Logistic Regression Binary outcomes The logit and inverse logit interpreting coefficients and odds ratios Maximum likelihood estimation Problem of separation Evaluating
More informationUnit 9: Inferences for Proportions and Count Data
Unit 9: Inferences for Proportions and Count Data Statistics 571: Statistical Methods Ramón V. León 12/15/2008 Unit 9  Stat 571  Ramón V. León 1 Large Sample Confidence Interval for Proportion ( pˆ p)
More informationModels 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 informationZERO INFLATED POISSON REGRESSION
STAT 6500 ZERO INFLATED POISSON REGRESSION FINAL PROJECT DEC 6 th, 2013 SUN JEON DEPARTMENT OF SOCIOLOGY UTAH STATE UNIVERSITY POISSON REGRESSION REVIEW INTRODUCING  ZEROINFLATED POISSON REGRESSION SAS
More information2/26/2017. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2
PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 When and why do we use logistic regression? Binary Multinomial Theory behind logistic regression Assessing the model Assessing predictors
More informationGeneralized Linear Models for NonNormal Data
Generalized Linear Models for NonNormal Data Today s Class: 3 parts of a generalized model Models for binary outcomes Complications for generalized multivariate or multilevel models SPLH 861: Lecture
More informationComparing IRT with Other Models
Comparing IRT with Other Models Lecture #14 ICPSR Item Response Theory Workshop Lecture #14: 1of 45 Lecture Overview The final set of slides will describe a parallel between IRT and another commonly used
More informationUsing Estimating Equations for Spatially Correlated A
Using Estimating Equations for Spatially Correlated Areal Data December 8, 2009 Introduction GEEs Spatial Estimating Equations Implementation Simulation Conclusion Typical Problem Assess the relationship
More informationThreeWay Contingency Tables
Newsom PSY 50/60 Categorical Data Analysis, Fall 06 ThreeWay Contingency Tables Threeway contingency tables involve three binary or categorical variables. I will stick mostly to the binary case to keep
More informationHypothesis Testing, Power, Sample Size and Confidence Intervals (Part 2)
Hypothesis Testing, Power, Sample Size and Confidence Intervals (Part 2) B.H. Robbins Scholars Series June 23, 2010 1 / 29 Outline Ztest χ 2 test Confidence Interval Sample size and power Relative effect
More informationInvestigating Models with Two or Three Categories
Ronald H. Heck and Lynn N. Tabata 1 Investigating Models with Two or Three Categories For the past few weeks we have been working with discriminant analysis. Let s now see what the same sort of model might
More informationStatistical Modelling with Stata: Binary Outcomes
Statistical Modelling with Stata: Binary Outcomes Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester 21/11/2017 Crosstabulation Exposed Unexposed Total Cases a b a + b Controls
More information9 Generalized Linear Models
9 Generalized Linear Models The Generalized Linear Model (GLM) is a model which has been built to include a wide range of different models you already know, e.g. ANOVA and multiple linear regression models
More informationGeneralized Linear Model under the Extended Negative Multinomial Model and Cancer Incidence
Generalized Linear Model under the Extended Negative Multinomial Model and Cancer Incidence Sunil Kumar Dhar Center for Applied Mathematics and Statistics, Department of Mathematical Sciences, New Jersey
More informationLogistic regression modeling the probability of success
Logistic regression modeling the probability of success Regression models are usually thought of as only being appropriate for target variables that are continuous Is there any situation where we might
More informationGeneralized linear models for binary data. A better graphical exploratory data analysis. The simple linear logistic regression model
Stat 3302 (Spring 2017) Peter F. Craigmile Simple linear logistic regression (part 1) [Dobson and Barnett, 2008, Sections 7.1 7.3] Generalized linear models for binary data Beetles doseresponse example
More informationMachine Learning Linear Classification. Prof. Matteo Matteucci
Machine Learning Linear Classification Prof. Matteo Matteucci Recall from the first lecture 2 X R p Regression Y R Continuous Output X R p Y {Ω 0, Ω 1,, Ω K } Classification Discrete Output X R p Y (X)
More informationNegative Multinomial Model and Cancer. Incidence
Generalized Linear Model under the Extended Negative Multinomial Model and Cancer Incidence S. Lahiri & Sunil K. Dhar Department of Mathematical Sciences, CAMS New Jersey Institute of Technology, Newar,
More informationModel 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 informationHierarchical Generalized Linear Models. ERSH 8990 REMS Seminar on HLM Last Lecture!
Hierarchical Generalized Linear Models ERSH 8990 REMS Seminar on HLM Last Lecture! Hierarchical Generalized Linear Models Introduction to generalized models Models for binary outcomes Interpreting parameter
More informationTests for Two Correlated Proportions in a Matched Case Control Design
Chapter 155 Tests for Two Correlated Proportions in a Matched Case Control Design Introduction A 2byM casecontrol study investigates a risk factor relevant to the development of a disease. A population
More information12 Generalized linear models
12 Generalized linear models In this chapter, we combine regression models with other parametric probability models like the binomial and Poisson distributions. Binary responses In many situations, we
More informationST3241 Categorical Data Analysis I Generalized Linear Models. Introduction and Some Examples
ST3241 Categorical Data Analysis I Generalized Linear Models Introduction and Some Examples 1 Introduction We have discussed methods for analyzing associations in twoway and threeway tables. Now we will
More informationChapter 1 Statistical Inference
Chapter 1 Statistical Inference causal inference To infer causality, you need a randomized experiment (or a huge observational study and lots of outside information). inference to populations Generalizations
More informationLinear Regression With Special Variables
Linear Regression With Special Variables Junhui Qian December 21, 2014 Outline Standardized Scores Quadratic Terms Interaction Terms Binary Explanatory Variables Binary Choice Models Standardized Scores:
More informationCOMPLEMENTARY LOGLOG MODEL
COMPLEMENTARY LOGLOG MODEL Under the assumption of binary response, there are two alternatives to logit model: probit model and complementaryloglog model. They all follow the same form π ( x) =Φ ( α
More informationExtensions of Cox Model for NonProportional Hazards Purpose
PhUSE 2013 Paper SP07 Extensions of Cox Model for NonProportional Hazards Purpose Jadwiga Borucka, PAREXEL, Warsaw, Poland ABSTRACT Cox proportional hazard model is one of the most common methods used
More informationCorrelation and simple linear regression S5
Basic medical statistics for clinical and eperimental research Correlation and simple linear regression S5 Katarzyna Jóźwiak k.jozwiak@nki.nl November 15, 2017 1/41 Introduction Eample: Brain size and
More informationConfidence Intervals for the Odds Ratio in Logistic Regression with One Binary X
Chapter 864 Confidence Intervals for the Odds Ratio in Logistic Regression with One Binary X Introduction Logistic regression expresses the relationship between a binary response variable and one or more
More informationHypothesis testing, part 2. With some material from Howard Seltman, Blase Ur, Bilge Mutlu, Vibha Sazawal
Hypothesis testing, part 2 With some material from Howard Seltman, Blase Ur, Bilge Mutlu, Vibha Sazawal 1 CATEGORICAL IV, NUMERIC DV 2 Independent samples, one IV # Conditions Normal/Parametric Nonparametric
More informationSections 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 informationModels 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 informationGeneralized 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 informationContinuous Time Survival in Latent Variable Models
Continuous Time Survival in Latent Variable Models Tihomir Asparouhov 1, Katherine Masyn 2, Bengt Muthen 3 Muthen & Muthen 1 University of California, Davis 2 University of California, Los Angeles 3 Abstract
More informationA note on R 2 measures for Poisson and logistic regression models when both models are applicable
Journal of Clinical Epidemiology 54 (001) 99 103 A note on R measures for oisson and logistic regression models when both models are applicable Martina Mittlböck, Harald Heinzl* Department of Medical Computer
More informationDependent Variable Q83: Attended meetings of your town or city council (0=no, 1=yes)
Logistic Regression Kristi Andrasik COM 731 Spring 2017. MODEL all data drawn from the 2006 National Community Survey (class data set) BLOCK 1 (Stepwise) Lifestyle Values Q7: Value work Q8: Value friends
More informationResearch Methodology: Tools
MSc Business Administration Research Methodology: Tools Applied Data Analysis (with SPSS) Lecture 05: Contingency Analysis March 2014 Prof. Dr. Jürg Schwarz Lic. phil. Heidi Bruderer Enzler Contents Slide
More informationCASE STUDY: Bayesian Incidence Analyses from CrossSectional Data with Multiple Markers of Disease Severity. Outline:
CASE STUDY: Bayesian Incidence Analyses from CrossSectional Data with Multiple Markers of Disease Severity Outline: 1. NIEHS Uterine Fibroid Study Design of Study Scientific Questions Difficulties 2.
More informationGeneralized Linear Models (GLZ)
Generalized Linear Models (GLZ) Generalized Linear Models (GLZ) are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the
More informationExact McNemar s Test and Matching Confidence Intervals Michael P. Fay April 25,
Exact McNemar s Test and Matching Confidence Intervals Michael P. Fay April 25, 2016 1 McNemar s Original Test Consider paired binary response data. For example, suppose you have twins randomized to two
More informationTimeInvariant Predictors in Longitudinal Models
TimeInvariant Predictors in Longitudinal Models Today s Topics: What happens to missing predictors Effects of timeinvariant predictors Fixed vs. systematically varying vs. random effects Model building
More informationLogistic regression: Miscellaneous topics
Logistic regression: Miscellaneous topics April 11 Introduction We have covered two approaches to inference for GLMs: the Wald approach and the likelihood ratio approach I claimed that the likelihood ratio
More informationESP 178 Applied Research Methods. 2/23: Quantitative Analysis
ESP 178 Applied Research Methods 2/23: Quantitative Analysis Data Preparation Data coding create codebook that defines each variable, its response scale, how it was coded Data entry for mail surveys and
More informationPOLI 7050 Spring 2008 March 5, 2008 Unordered Response Models II
POLI 7050 Spring 2008 March 5, 2008 Unordered Response Models II Introduction Today we ll talk about interpreting MNL and CL models. We ll start with general issues of model fit, and then get to variable
More informationConfidence Intervals for the Odds Ratio in Logistic Regression with Two Binary X s
Chapter 866 Confidence Intervals for the Odds Ratio in Logistic Regression with Two Binary X s Introduction Logistic regression expresses the relationship between a binary response variable and one or
More informationMediation for the 21st Century
Mediation for the 21st Century Ross Boylan ross@biostat.ucsf.edu Center for Aids Prevention Studies and Division of Biostatistics University of California, San Francisco Mediation for the 21st Century
More informationBinary Choice Models Probit & Logit. = 0 with Pr = 0 = 1. decisionmaking purchase of durable consumer products unemployment
BINARY CHOICE MODELS Y ( Y ) ( Y ) 1 with Pr = 1 = P = 0 with Pr = 0 = 1 P Examples: decisionmaking purchase of durable consumer products unemployment Estimation with OLS? Yi = Xiβ + εi Problems: nonsense
More informationGlossary for the Triola Statistics Series
Glossary for the Triola Statistics Series Absolute deviation The measure of variation equal to the sum of the deviations of each value from the mean, divided by the number of values Acceptance sampling
More informationBIAS OF MAXIMUMLIKELIHOOD ESTIMATES IN LOGISTIC AND COX REGRESSION MODELS: A COMPARATIVE SIMULATION STUDY
BIAS OF MAXIMUMLIKELIHOOD ESTIMATES IN LOGISTIC AND COX REGRESSION MODELS: A COMPARATIVE SIMULATION STUDY Ingo Langner 1, Ralf Bender 2, Rebecca LenzTönjes 1, Helmut Küchenhoff 2, Maria Blettner 2 1
More informationContrasting 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 informationLecture 10: Alternatives to OLS with limited dependent variables. PEA vs APE Logit/Probit Poisson
Lecture 10: Alternatives to OLS with limited dependent variables PEA vs APE Logit/Probit Poisson PEA vs APE PEA: partial effect at the average The effect of some x on y for a hypothetical case with sample
More informationInference 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 informationRon Heck, Fall Week 8: Introducing Generalized Linear Models: Logistic Regression 1 (Replaces prior revision dated October 20, 2011)
Ron Heck, Fall 2011 1 EDEP 768E: Seminar in Multilevel Modeling rev. January 3, 2012 (see footnote) Week 8: Introducing Generalized Linear Models: Logistic Regression 1 (Replaces prior revision dated October
More informationClassification: Linear Discriminant Analysis
Classification: Linear Discriminant Analysis Discriminant analysis uses sample information about individuals that are known to belong to one of several populations for the purposes of classification. Based
More informationChapter 14 Logistic Regression, Poisson Regression, and Generalized Linear Models
Chapter 14 Logistic Regression, Poisson Regression, and Generalized Linear Models 許湘伶 Applied Linear Regression Models (Kutner, Nachtsheim, Neter, Li) hsuhl (NUK) LR Chap 10 1 / 29 14.1 Regression Models
More informationLinear Regression Models P8111
Linear Regression Models P8111 Lecture 25 Jeff Goldsmith April 26, 2016 1 of 37 Today s Lecture Logistic regression / GLMs Model framework Interpretation Estimation 2 of 37 Linear regression Course started
More informationRegression models for multivariate ordered responses via the Plackett distribution
Journal of Multivariate Analysis 99 (2008) 2472 2478 www.elsevier.com/locate/jmva Regression models for multivariate ordered responses via the Plackett distribution A. Forcina a,, V. Dardanoni b a Dipartimento
More informationHypothesis Testing hypothesis testing approach
Hypothesis Testing In this case, we d be trying to form an inference about that neighborhood: Do people there shop more often those people who are members of the larger population To ascertain this, we
More informationModelling Binary Outcomes 21/11/2017
Modelling Binary Outcomes 21/11/2017 Contents 1 Modelling Binary Outcomes 5 1.1 Crosstabulation.................................... 5 1.1.1 Measures of Effect............................... 6 1.1.2 Limitations
More informationLISA Short Course Series Generalized Linear Models (GLMs) & Categorical Data Analysis (CDA) in R. Liang (Sally) Shan Nov. 4, 2014
LISA Short Course Series Generalized Linear Models (GLMs) & Categorical Data Analysis (CDA) in R Liang (Sally) Shan Nov. 4, 2014 L Laboratory for Interdisciplinary Statistical Analysis LISA helps VT researchers
More informationStat/F&W Ecol/Hort 572 Review Points Ané, Spring 2010
1 Linear models Y = Xβ + ɛ with ɛ N (0, σ 2 e) or Y N (Xβ, σ 2 e) where the model matrix X contains the information on predictors and β includes all coefficients (intercept, slope(s) etc.). 1. Number of
More informationCHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA
Examples: Multilevel Modeling With Complex Survey Data CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA Complex survey data refers to data obtained by stratification, cluster sampling and/or
More informationSTAT5044: Regression and Anova
STAT5044: Regression and Anova Inyoung Kim 1 / 18 Outline 1 Logistic regression for Binary data 2 Poisson regression for Count data 2 / 18 GLM Let Y denote a binary response variable. Each observation
More informationBinomial Model. Lecture 10: Introduction to Logistic Regression. Logistic Regression. Binomial Distribution. n independent trials
Lecture : Introduction to Logistic Regression Ani Manichaikul amanicha@jhsph.edu 2 May 27 Binomial Model n independent trials (e.g., coin tosses) p = probability of success on each trial (e.g., p =! =
More informationThe STS Surgeon Composite Technical Appendix
The STS Surgeon Composite Technical Appendix Overview Surgeonspecific riskadjusted operative operative mortality and major complication rates were estimated using a bivariate randomeffects logistic
More informationON GOODNESSOFFIT OF LOGISTIC REGRESSION MODEL YING LIU. M.S., University of Rhode Island, 2003 M.S., Henan Normal University, 2000
ON GOODNESSOFFIT OF LOGISTIC REGRESSION MODEL by YING LIU M.S., University of Rhode Island, 2003 M.S., Henan Normal University, 2000 AN ABSTRACT OF A DISSERTATION submitted in partial fulfillment of
More informationVIII. ANCOVA. A. Introduction
VIII. ANCOVA A. Introduction In most experiments and observational studies, additional information on each experimental unit is available, information besides the factors under direct control or of interest.
More informationDeriving 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 informationTied survival times; estimation of survival probabilities
Tied survival times; estimation of survival probabilities Patrick Breheny November 5 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/22 Introduction Tied survival times Introduction Breslow approximation
More informationMS&E 226: Small Data
MS&E 226: Small Data Lecture 6: Model complexity scores (v3) Ramesh Johari ramesh.johari@stanford.edu Fall 2015 1 / 34 Estimating prediction error 2 / 34 Estimating prediction error We saw how we can estimate
More informationMixture Modeling in Mplus
Mixture Modeling in Mplus Gitta Lubke University of Notre Dame VU University Amsterdam Mplus Workshop John s Hopkins 2012 G. Lubke, ND, VU Mixture Modeling in Mplus 1/89 Outline 1 Overview 2 Latent Class
More informationEDF 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 informationSupplemental Materials. In the main text, we recommend graphing physiological values for individual dyad
1 Supplemental Materials Graphing Values for Individual Dyad Members over Time In the main text, we recommend graphing physiological values for individual dyad members over time to aid in the decision
More informationEstimated Precision for Predictions from Generalized Linear Models in Sociological Research
Quality & Quantity 34: 137 152, 2000. 2000 Kluwer Academic Publishers. Printed in the Netherlands. 137 Estimated Precision for Predictions from Generalized Linear Models in Sociological Research TIM FUTING
More informationLecture 8 Stat D. Gillen
Statistics 255  Survival Analysis Presented February 23, 2016 Dan Gillen Department of Statistics University of California, Irvine 8.1 Example of two ways to stratify Suppose a confounder C has 3 levels
More informationABSTRACT INTRODUCTION. SESUG Paper
SESUG Paper 1402017 Backward Variable Selection for Logistic Regression Based on Percentage Change in Odds Ratio Evan Kwiatkowski, University of North Carolina at Chapel Hill; Hannah Crooke, PAREXEL International
More informationClassification 1: Linear regression of indicators, linear discriminant analysis
Classification 1: Linear regression of indicators, linear discriminant analysis Ryan Tibshirani Data Mining: 36462/36662 April 2 2013 Optional reading: ISL 4.1, 4.2, 4.4, ESL 4.1 4.3 1 Classification
More informationDescription Syntax for predict Menu for predict Options for predict Remarks and examples Methods and formulas References Also see
Title stata.com logistic postestimation Postestimation tools for logistic Description Syntax for predict Menu for predict Options for predict Remarks and examples Methods and formulas References Also see
More informationLecture 16 Solving GLMs via IRWLS
Lecture 16 Solving GLMs via IRWLS 09 November 2015 Taylor B. Arnold Yale Statistics STAT 312/612 Notes problem set 5 posted; due next class problem set 6, November 18th Goals for today fixed PCA example
More informationBivariate Data: Graphical Display The scatterplot is the basic tool for graphically displaying bivariate quantitative data.
Bivariate Data: Graphical Display The scatterplot is the basic tool for graphically displaying bivariate quantitative data. Example: Some investors think that the performance of the stock market in January
More informationIntroduction to Survey Analysis!
Introduction to Survey Analysis! Professor Ron Fricker! Naval Postgraduate School! Monterey, California! Reading Assignment:! 2/22/13 None! 1 Goals for this Lecture! Introduction to analysis for surveys!
More information1 Introduction A common problem in categorical data analysis is to determine the effect of explanatory variables V on a binary outcome D of interest.
Conditional and Unconditional Categorical Regression Models with Missing Covariates Glen A. Satten and Raymond J. Carroll Λ December 4, 1999 Abstract We consider methods for analyzing categorical regression
More informationLecture 11 Multiple Linear Regression
Lecture 11 Multiple Linear Regression STAT 512 Spring 2011 Background Reading KNNL: 6.16.5 111 Topic Overview Review: Multiple Linear Regression (MLR) Computer Science Case Study 112 Multiple Regression
More informationAnalytic Methods for Applied Epidemiology: Framework and Contingency Table Analysis
Analytic Methods for Applied Epidemiology: Framework and Contingency Table Analysis 2014 Maternal and Child Health Epidemiology Training PreTraining Webinar: Friday, May 16 24pm Eastern Kristin Rankin,
More informationPseudoscore confidence intervals for parameters in discrete statistical models
Biometrika Advance Access published January 14, 2010 Biometrika (2009), pp. 1 8 C 2009 Biometrika Trust Printed in Great Britain doi: 10.1093/biomet/asp074 Pseudoscore confidence intervals for parameters
More informationAttributable Risk Function in the Proportional Hazards Model
UW Biostatistics Working Paper Series 5312005 Attributable Risk Function in the Proportional Hazards Model Ying Qing Chen Fred Hutchinson Cancer Research Center, yqchen@u.washington.edu Chengcheng Hu
More informationSAS 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 informationLinear Methods for Prediction
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 informationSTAT 331. Accelerated Failure Time Models. Previously, we have focused on multiplicative intensity models, where
STAT 331 Accelerated Failure Time Models Previously, we have focused on multiplicative intensity models, where h t z) = h 0 t) g z). These can also be expressed as H t z) = H 0 t) g z) or S t z) = e Ht
More informationFlexible mediation analysis in the presence of nonlinear relations: beyond the mediation formula.
FACULTY OF PSYCHOLOGY AND EDUCATIONAL SCIENCES Flexible mediation analysis in the presence of nonlinear relations: beyond the mediation formula. Modern Modeling Methods (M 3 ) Conference Beatrijs Moerkerke
More informationSTAT 5500/6500 Conditional Logistic Regression for Matched Pairs
STAT 5500/6500 Conditional Logistic Regression for Matched Pairs The data for the tutorial came from support.sas.com, The LOGISTIC Procedure: Conditional Logistic Regression for Matched Pairs Data :: SAS/STAT(R)
More informationMS&E 226: Small Data
MS&E 226: Small Data Lecture 9: Logistic regression (v2) Ramesh Johari ramesh.johari@stanford.edu 1 / 28 Regression methods for binary outcomes 2 / 28 Binary outcomes For the duration of this lecture suppose
More information