Notating the Multilevel Longitudinal Model. Multilevel Modeling of Longitudinal Data. Notating (cont.) Notating (cont.)
|
|
- Leo Fitzgerald
- 7 years ago
- Views:
Transcription
1 Notating the Multilevel Modeling of Longitudinal Data Recall the typical -level model Y ij = γ 00 + (γ 0 + u j )X ij + u 0j + e ij Dr. J. Kyle Roberts Southern Methodist University Simmons School of Education and Human Development Department of Teaching and Learning For the multilevel repeated measures model, we have measurement occasions nested inside individuals. Y ti = β 00 + (β 0 + u j )T ti + u 0i + e ti where T ti is a variable designating the time at which Y ti is measured Notating (cont.) Notating (cont.) From before, we can take the full mixed model. Y ti = β 00 + (β 0 + u j )T ti + u 0i + e ti and break it into levels such that the measurement level is Y ti = π 0i + π i T ti + e ti When we add variables at the measurement level into these models, they are referred to as time-varying covariates. Supposing that Y ti is student GPA at time t. A time-varying covariate could be the number of hours of coursework the student was taking at time t. This would be modeled as: and the student level is: Y ti = β 00 + (β 0 + u j )T ti + β 0 X ti + u 0i + e ti π 0i = β 00 + u 0i π i = β 0 + u i Variables at the student level would be referred to as time-invariant covariates, such as gender. These would be modeled as: This model is also referred to as the null model in the multilevel repeated measures as it is the reference model from which we will test all future models. Y ti = β 00 + (β 0 + u j )T ti + β 0 X ti + β 0 Z i + u 0i + e ti
2 Data Generation > par(mfrow = c(, )) > boxplot(reading ~, data = read.data, xlab = "Weeks of Instr + ylab = "Reading Score") > boxplot(reading ~ id, data = read.data, xlab = "Student ID", + ylab = "Reading Score") > set.seed(00) > read.data <- data.frame(expand.grid( = 0:, + id = :0), treatment = rep(c("control", "treat"), + each = 0), reading = c(sort(rnorm(0,, + 0)), sort(rnorm(0,, 0)), sort(rnorm(0, +, 0)), sort(rnorm(0,, 0)), sort(rnorm(0, + 0, 0)), sort(rnorm(0,, )), sort(rnorm(0, +, )), sort(rnorm(0,, )), sort(rnorm(0, +, )), sort(rnorm(0,, )))) > read.data <- factor(read.data) Reading Score Reading Score Weeks of Instruction Student ID > print(xyplot(reading ~ id, data = read.data, Repeated Measures ANOVA reading 0 > summary(aov(reading ~ factor() + Error(id), + data = read.data)) Error: id Residuals 0 Error: Within factor() 0..0.e-0 Residuals.
3 Add as a Between Subjects Factor The Multilevel Time Series > (m0 <- lmer(reading ~ + ( id), read.data)) > summary(aov(reading ~ factor() * treatment + + Error(id), data = read.data)) Error: id treatment Residuals 0 Error: Within factor() 0..0.e- factor():treatment.0..0e-0 Residuals 0. Formula: reading ~ + ( id) id (Intercept) Residual.. (Intercept) (Intr) -0. The Multilevel Time Series (cont.) Adding a treatment effect > (m <- lmer(reading ~ + treatment + ( + id), read.data)) > coef(m0) (Intercept) Formula: reading ~ + treatment + ( id) id (Intercept) Residual.. (Intercept) treatmenttreat (Intr)
4 Adding a treatment effect (cont.) Adding an interaction effect > (m <- lmer(reading ~ * treatment + ( + id), read.data)) > coef(m) (Intercept) treatmenttreat Formula: reading ~ * treatment + ( id) id (Intercept) Residual.0. (Intercept) treatmenttreat :treatmenttreat Adding an interaction effect (cont.) > coef(m) (Intr) trtmnt -0. treatmnttrt wks:trtmntt Comparing Model Fit (Intercept) treatmenttreat :treatmenttreat > anova(m0, m, m) Models: m0: reading ~ + ( id) m: reading ~ + treatment + ( id) m: reading ~ * treatment + ( id) Df AIC BIC loglik Chisq Chi Df Pr(>Chisq) m m m
5 Interaction Plot > interaction.plot(read.data$, read.data$treatment, + fitted(m), xlab = "Weeks", ylab = "Reading", + lwd =, lty =, col = c("black", "grey")) Growth Trajectories for m0 > print(xyplot(fitted(m0) ~ id, read.data, Reading read.data$treatment treat control fitted(m0) 0 Weeks Growth Trajectories for m > print(xyplot(fitted(m) ~ id, read.data, fitted(m) 0
Introduction to Hierarchical Linear Modeling with R
Introduction to Hierarchical Linear Modeling with R 5 10 15 20 25 5 10 15 20 25 13 14 15 16 40 30 20 10 0 40 30 20 10 9 10 11 12-10 SCIENCE 0-10 5 6 7 8 40 30 20 10 0-10 40 1 2 3 4 30 20 10 0-10 5 10 15
More informationStatistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Linear Models in R Regression Regression analysis is the appropriate
More informationE(y i ) = x T i β. yield of the refined product as a percentage of crude specific gravity vapour pressure ASTM 10% point ASTM end point in degrees F
Random and Mixed Effects Models (Ch. 10) Random effects models are very useful when the observations are sampled in a highly structured way. The basic idea is that the error associated with any linear,
More informationSAS Syntax and Output for Data Manipulation:
Psyc 944 Example 5 page 1 Practice with Fixed and Random Effects of Time in Modeling Within-Person Change The models for this example come from Hoffman (in preparation) chapter 5. We will be examining
More informationIntroducing the Multilevel Model for Change
Department of Psychology and Human Development Vanderbilt University GCM, 2010 1 Multilevel Modeling - A Brief Introduction 2 3 4 5 Introduction In this lecture, we introduce the multilevel model for change.
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 informationMilk Data Analysis. 1. Objective Introduction to SAS PROC MIXED Analyzing protein milk data using STATA Refit protein milk data using PROC MIXED
1. Objective Introduction to SAS PROC MIXED Analyzing protein milk data using STATA Refit protein milk data using PROC MIXED 2. Introduction to SAS PROC MIXED The MIXED procedure provides you with flexibility
More informationDEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9
DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,
More informationA Handbook of Statistical Analyses Using R. Brian S. Everitt and Torsten Hothorn
A Handbook of Statistical Analyses Using R Brian S. Everitt and Torsten Hothorn CHAPTER 6 Logistic Regression and Generalised Linear Models: Blood Screening, Women s Role in Society, and Colonic Polyps
More informationThe Latent Variable Growth Model In Practice. Individual Development Over Time
The Latent Variable Growth Model In Practice 37 Individual Development Over Time y i = 1 i = 2 i = 3 t = 1 t = 2 t = 3 t = 4 ε 1 ε 2 ε 3 ε 4 y 1 y 2 y 3 y 4 x η 0 η 1 (1) y ti = η 0i + η 1i x t + ε ti
More informationBasic Statistics and Data Analysis for Health Researchers from Foreign Countries
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
More informationThis can dilute the significance of a departure from the null hypothesis. We can focus the test on departures of a particular form.
One-Degree-of-Freedom Tests Test for group occasion interactions has (number of groups 1) number of occasions 1) degrees of freedom. This can dilute the significance of a departure from the null hypothesis.
More informationLongitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations
Research Article TheScientificWorldJOURNAL (2011) 11, 42 76 TSW Child Health & Human Development ISSN 1537-744X; DOI 10.1100/tsw.2011.2 Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts,
More informationI L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Beckman HLM Reading Group: Questions, Answers and Examples Carolyn J. Anderson Department of Educational Psychology I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Linear Algebra Slide 1 of
More informationFamily economics data: total family income, expenditures, debt status for 50 families in two cohorts (A and B), annual records from 1990 1995.
Lecture 18 1. Random intercepts and slopes 2. Notation for mixed effects models 3. Comparing nested models 4. Multilevel/Hierarchical models 5. SAS versions of R models in Gelman and Hill, chapter 12 1
More informationStatistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova
More informationdata visualization and regression
data visualization and regression Sepal.Length 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 I. setosa I. versicolor I. virginica I. setosa I. versicolor I. virginica Species Species
More informationIntroduction to Longitudinal Data Analysis
Introduction to Longitudinal Data Analysis Longitudinal Data Analysis Workshop Section 1 University of Georgia: Institute for Interdisciplinary Research in Education and Human Development Section 1: Introduction
More informationPaired Comparison Models. Paired Comparison Preference Models. The prefmod Package: Part I Some Examples. Paired Comparisons.
Paired Comparison Models Paired Comparison Models Paired Comparison Models General Considerations: Paired Comparison Preference Models The prefmod Package: Part I Some Examples Regina Dittrich & Reinhold
More informationLecture 5 : The Poisson Distribution
Lecture 5 : The Poisson Distribution Jonathan Marchini November 10, 2008 1 Introduction Many experimental situations occur in which we observe the counts of events within a set unit of time, area, volume,
More informationElectronic Thesis and Dissertations UCLA
Electronic Thesis and Dissertations UCLA Peer Reviewed Title: A Multilevel Longitudinal Analysis of Teaching Effectiveness Across Five Years Author: Wang, Kairong Acceptance Date: 2013 Series: UCLA Electronic
More informationα α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More 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 informationThe 3-Level HLM Model
James H. Steiger Department of Psychology and Human Development Vanderbilt University Regression Modeling, 2009 1 2 Basic Characteristics of the 3-level Model Level-1 Model Level-2 Model Level-3 Model
More informationSPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
More informationLab 13: Logistic Regression
Lab 13: Logistic Regression Spam Emails Today we will be working with a corpus of emails received by a single gmail account over the first three months of 2012. Just like any other email address this account
More informationOverview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)
Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and
More informationPackage smoothhr. November 9, 2015
Encoding UTF-8 Type Package Depends R (>= 2.12.0),survival,splines Package smoothhr November 9, 2015 Title Smooth Hazard Ratio Curves Taking a Reference Value Version 1.0.2 Date 2015-10-29 Author Artur
More information# load in the files containing the methyaltion data and the source # code containing the SSRPMM functions
################ EXAMPLE ANALYSES TO ILLUSTRATE SS-RPMM ######################## # load in the files containing the methyaltion data and the source # code containing the SSRPMM functions # Note, the SSRPMM
More informationMIXED MODEL ANALYSIS USING R
Research Methods Group MIXED MODEL ANALYSIS USING R Using Case Study 4 from the BIOMETRICS & RESEARCH METHODS TEACHING RESOURCE BY Stephen Mbunzi & Sonal Nagda www.ilri.org/rmg www.worldagroforestrycentre.org/rmg
More information# For usage of the functions, it is necessary to install the "survival" and the "penalized" package.
###################################################################### ### R-script for the manuscript ### ### ### ### Survival models with preclustered ### ### gene groups as covariates ### ### ### ###
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 informationIllustration (and the use of HLM)
Illustration (and the use of HLM) Chapter 4 1 Measurement Incorporated HLM Workshop The Illustration Data Now we cover the example. In doing so we does the use of the software HLM. In addition, we will
More informationChapter 4 Models for Longitudinal Data
Chapter 4 Models for Longitudinal Data Longitudinal data consist of repeated measurements on the same subject (or some other experimental unit ) taken over time. Generally we wish to characterize the time
More informationLinda Staub & Alexandros Gekenidis
Seminar in Statistics: Survival Analysis Chapter 2 Kaplan-Meier Survival Curves and the Log- Rank Test Linda Staub & Alexandros Gekenidis March 7th, 2011 1 Review Outcome variable of interest: time until
More informationMultilevel Modeling in R, Using the nlme Package
Multilevel Modeling in R, Using the nlme Package William T. Hoyt (University of Wisconsin-Madison) David A. Kenny (University of Connecticut) March 21, 2013 Supplement to Kenny, D. A., & Hoyt, W. (2009)
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 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More information" 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 informationLecture 14: GLM Estimation and Logistic Regression
Lecture 14: GLM Estimation and Logistic Regression Dipankar Bandyopadhyay, Ph.D. BMTRY 711: Analysis of Categorical Data Spring 2011 Division of Biostatistics and Epidemiology Medical University of South
More informationAnalyzing Intervention Effects: Multilevel & Other Approaches. Simplest Intervention Design. Better Design: Have Pretest
Analyzing Intervention Effects: Multilevel & Other Approaches Joop Hox Methodology & Statistics, Utrecht Simplest Intervention Design R X Y E Random assignment Experimental + Control group Analysis: t
More informationLecture 15: mixed-effects logistic regression
Lecture 15: mixed-effects logistic regression 28 November 2007 In this lecture we ll learn about mixed-effects modeling for logistic regression. 1 Technical recap We moved from generalized linear models
More informationMixed-effects regression and eye-tracking data
Mixed-effects regression and eye-tracking data Lecture 2 of advanced regression methods for linguists Martijn Wieling and Jacolien van Rij Seminar für Sprachwissenschaft University of Tübingen LOT Summer
More informationAn Introduction to Modeling Longitudinal Data
An Introduction to Modeling Longitudinal Data Session I: Basic Concepts and Looking at Data Robert Weiss Department of Biostatistics UCLA School of Public Health robweiss@ucla.edu August 2010 Robert Weiss
More informationLongitudinal Meta-analysis
Quality & Quantity 38: 381 389, 2004. 2004 Kluwer Academic Publishers. Printed in the Netherlands. 381 Longitudinal Meta-analysis CORA J. M. MAAS, JOOP J. HOX and GERTY J. L. M. LENSVELT-MULDERS Department
More informationMultilevel Models for Longitudinal Data. Fiona Steele
Multilevel Models for Longitudinal Data Fiona Steele Aims of Talk Overview of the application of multilevel (random effects) models in longitudinal research, with examples from social research Particular
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationClass 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2
University of California, Berkeley Prof. Ken Chay Department of Economics Fall Semester, 005 ECON 14 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE # Question 1: a. Below are the scatter plots of hourly wages
More informationRegression and Programming in R. Anja Bråthen Kristoffersen Biomedical Research Group
Regression and Programming in R Anja Bråthen Kristoffersen Biomedical Research Group R Reference Card http://cran.r-project.org/doc/contrib/short-refcard.pdf Simple linear regression Describes the relationship
More informationPsychology 405: Psychometric Theory Homework on Factor analysis and structural equation modeling
Psychology 405: Psychometric Theory Homework on Factor analysis and structural equation modeling William Revelle Department of Psychology Northwestern University Evanston, Illinois USA June, 2014 1 / 20
More informationMultiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
More informationIndices of Model Fit STRUCTURAL EQUATION MODELING 2013
Indices of Model Fit STRUCTURAL EQUATION MODELING 2013 Indices of Model Fit A recommended minimal set of fit indices that should be reported and interpreted when reporting the results of SEM analyses:
More informationInteraction between quantitative predictors
Interaction between quantitative predictors In a first-order 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 informationUsing splines in regression
Using splines in regression Author: Nicholas G Reich, Jeff Goldsmith This material is part of the statsteachr project Made available under the Creative Commons Attribution-ShareAlike 3.0 Unported License:
More informationBasic Statistical and Modeling Procedures Using SAS
Basic Statistical and Modeling Procedures Using SAS One-Sample Tests The statistical procedures illustrated in this handout use two datasets. The first, Pulse, has information collected in a classroom
More informationExploratory Data Analysis
Goals of EDA Relationship between mean response and covariates (including time). Variance, correlation structure, individual-level heterogeneity. Guidelines for graphical displays of longitudinal data
More informationRandom effects and nested models with SAS
Random effects and nested models with SAS /************* classical2.sas ********************* Three levels of factor A, four levels of B Both fixed Both random A fixed, B random B nested within A ***************************************************/
More information12.5: CHI-SQUARE GOODNESS OF FIT TESTS
125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability
More informationOutline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation
More informationWeek 5: Multiple Linear Regression
BUS41100 Applied Regression Analysis Week 5: Multiple Linear Regression Parameter estimation and inference, forecasting, diagnostics, dummy variables Robert B. Gramacy The University of Chicago Booth School
More informationINTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA)
INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the one-way ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of
More informationModule 5: Introduction to Multilevel Modelling. R Practical. Introduction to the Scottish Youth Cohort Trends Dataset. Contents
Introduction Module 5: Introduction to Multilevel Modelling R Practical Camille Szmaragd and George Leckie 1 Centre for Multilevel Modelling Some of the sections within this module have online quizzes
More informationModule 5: Introduction to Multilevel Modelling SPSS Practicals Chris Charlton 1 Centre for Multilevel Modelling
Module 5: Introduction to Multilevel Modelling SPSS Practicals Chris Charlton 1 Centre for Multilevel Modelling Pre-requisites Modules 1-4 Contents P5.1 Comparing Groups using Multilevel Modelling... 4
More informationR 2 -type Curves for Dynamic Predictions from Joint Longitudinal-Survival Models
Faculty of Health Sciences R 2 -type Curves for Dynamic Predictions from Joint Longitudinal-Survival Models Inference & application to prediction of kidney graft failure Paul Blanche joint work with M-C.
More information1 Basic ANOVA concepts
Math 143 ANOVA 1 Analysis of Variance (ANOVA) Recall, when we wanted to compare two population means, we used the 2-sample t procedures. Now let s expand this to compare k 3 population means. As with the
More informationThe Basic Two-Level Regression Model
2 The Basic Two-Level Regression Model The multilevel regression model has become known in the research literature under a variety of names, such as random coefficient model (de Leeuw & Kreft, 1986; Longford,
More informationA LONGITUDINAL AND SURVIVAL MODEL WITH HEALTH CARE USAGE FOR INSURED ELDERLY. Workshop
A LONGITUDINAL AND SURVIVAL MODEL WITH HEALTH CARE USAGE FOR INSURED ELDERLY Ramon Alemany Montserrat Guillén Xavier Piulachs Lozada Riskcenter - IREA Universitat de Barcelona http://www.ub.edu/riskcenter
More information5. Multiple regression
5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful
More informationStatistiek II. John Nerbonne. October 1, 2010. Dept of Information Science j.nerbonne@rug.nl
Dept of Information Science j.nerbonne@rug.nl October 1, 2010 Course outline 1 One-way ANOVA. 2 Factorial ANOVA. 3 Repeated measures ANOVA. 4 Correlation and regression. 5 Multiple regression. 6 Logistic
More informationRidge Regression. Patrick Breheny. September 1. Ridge regression Selection of λ Ridge regression in R/SAS
Ridge Regression Patrick Breheny September 1 Patrick Breheny BST 764: Applied Statistical Modeling 1/22 Ridge regression: Definition Definition and solution Properties As mentioned in the previous lecture,
More information1 Simple Linear Regression I Least Squares Estimation
Simple Linear Regression I Least Squares Estimation Textbook Sections: 8. 8.3 Previously, we have worked with a random variable x that comes from a population that is normally distributed with mean µ and
More informationMATH 10: Elementary Statistics and Probability Chapter 5: Continuous Random Variables
MATH 10: Elementary Statistics and Probability Chapter 5: Continuous Random Variables Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,
More informationApplied Statistics. J. Blanchet and J. Wadsworth. Institute of Mathematics, Analysis, and Applications EPF Lausanne
Applied Statistics J. Blanchet and J. Wadsworth Institute of Mathematics, Analysis, and Applications EPF Lausanne An MSc Course for Applied Mathematicians, Fall 2012 Outline 1 Model Comparison 2 Model
More informationViewing Ecological data using R graphics
Biostatistics Illustrations in Viewing Ecological data using R graphics A.B. Dufour & N. Pettorelli April 9, 2009 Presentation of the principal graphics dealing with discrete or continuous variables. Course
More informationNormal Distribution. Definition A continuous random variable has a normal distribution if its probability density. f ( y ) = 1.
Normal Distribution Definition A continuous random variable has a normal distribution if its probability density e -(y -µ Y ) 2 2 / 2 σ function can be written as for < y < as Y f ( y ) = 1 σ Y 2 π Notation:
More informationAnalysis of ordinal data with cumulative link models estimation with the R-package ordinal
Analysis of ordinal data with cumulative link models estimation with the R-package ordinal Rune Haubo B Christensen June 28, 2015 1 Contents 1 Introduction 3 2 Cumulative link models 4 2.1 Fitting cumulative
More informationParametric and non-parametric statistical methods for the life sciences - Session I
Why nonparametric methods What test to use? Rank Tests Parametric and non-parametric statistical methods for the life sciences - Session I Liesbeth Bruckers Geert Molenberghs Interuniversity Institute
More informationHLM software has been one of the leading statistical packages for hierarchical
Introductory Guide to HLM With HLM 7 Software 3 G. David Garson HLM software has been one of the leading statistical packages for hierarchical linear modeling due to the pioneering work of Stephen Raudenbush
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationANOVA. February 12, 2015
ANOVA February 12, 2015 1 ANOVA models Last time, we discussed the use of categorical variables in multivariate regression. Often, these are encoded as indicator columns in the design matrix. In [1]: %%R
More informationWillett & Singer, 2003 October 13, 2003
Willett & Singer, 3 October 13, 3 '8 '87 '9 '97 '8 ' '87 '9 '97 '8 ' '87 '9 '97 ' Longitudinal Research: Present status and and future prospects John B. Willett & Judith D. Singer Harvard University Graduate
More informationHighlights the connections between different class of widely used models in psychological and biomedical studies. Multiple Regression
GLMM tutor Outline 1 Highlights the connections between different class of widely used models in psychological and biomedical studies. ANOVA Multiple Regression LM Logistic Regression GLM Correlated data
More informationChapter 2 Models With Multiple Random-effects Terms
Chapter 2 Models With Multiple Random-effects Terms The mixed models considered in the previous chapter had only one randomeffects term, which was a simple, scalar random-effects term, and a single fixed-effects
More informationMultiple Regression. Page 24
Multiple Regression Multiple regression is an extension of simple (bi-variate) regression. The goal of multiple regression is to enable a researcher to assess the relationship between a dependent (predicted)
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 informationGoodness of Fit Tests for Categorical Data: Comparing Stata, R and SAS
Goodness of Fit Tests for Categorical Data: Comparing Stata, R and SAS Rino Bellocco 1,2, Sc.D. Sara Algeri 1, MS 1 University of Milano-Bicocca, Milan, Italy & 2 Karolinska Institutet, Stockholm, Sweden
More informationTime Series Analysis
Time Series Analysis hm@imm.dtu.dk Informatics and Mathematical Modelling Technical University of Denmark DK-2800 Kgs. Lyngby 1 Outline of the lecture Identification of univariate time series models, cont.:
More informationIntroduction. Survival Analysis. Censoring. Plan of Talk
Survival Analysis Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 01/12/2015 Survival Analysis is concerned with the length of time before an event occurs.
More informationLogistic regression (with R)
Logistic regression (with R) Christopher Manning 4 November 2007 1 Theory We can transform the output of a linear regression to be suitable for probabilities by using a logit link function on the lhs as
More informationTime Series Analysis with R - Part I. Walter Zucchini, Oleg Nenadić
Time Series Analysis with R - Part I Walter Zucchini, Oleg Nenadić Contents 1 Getting started 2 1.1 Downloading and Installing R.................... 2 1.2 Data Preparation and Import in R.................
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 informationTests for Two Survival Curves Using Cox s Proportional Hazards Model
Chapter 730 Tests for Two Survival Curves Using Cox s Proportional Hazards Model Introduction A clinical trial is often employed to test the equality of survival distributions of two treatment groups.
More informationComparing Nested Models
Comparing Nested Models ST 430/514 Two models are nested if one model contains all the terms of the other, and at least one additional term. The larger model is the complete (or full) model, and the smaller
More informationProbability Calculator
Chapter 95 Introduction Most statisticians have a set of probability tables that they refer to in doing their statistical wor. This procedure provides you with a set of electronic statistical tables that
More information11. Analysis of Case-control Studies Logistic Regression
Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationGLM with a Gamma-distributed Dependent Variable
GLM with a Gamma-distributed Dependent Variable Paul E. Johnson October 6, 204 Introduction I started out to write about why the Gamma distribution in a GLM is useful. In the end, I ve found it difficult
More informationPackage lmertest. July 16, 2015
Type Package Title Tests in Linear Mixed Effects Models Version 2.0-29 Package lmertest July 16, 2015 Maintainer Alexandra Kuznetsova Depends R (>= 3.0.0), Matrix, stats, methods, lme4 (>=
More informationUsing R for Linear Regression
Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional
More information