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### 26-Logistic.WXP

Course: STAT 7034, Fall 2005
School: LSU
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Word Count: 500

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ON REGRESSION AN INDICATOR VARIABLE In this technique, the dependent variable (Y) is an indicator, and takes a value of either 0 or 1. This is called a binary response variable 1 Response 0 Independent Variable(s) Examples any two categories, any binomial or binary variable a) Success-failure, Gender (Male-female), mortality, presence-absence, pass-fail, etc. The results of a simple linear regression is a slope...

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ON REGRESSION AN INDICATOR VARIABLE In this technique, the dependent variable (Y) is an indicator, and takes a value of either 0 or 1. This is called a binary response variable 1 Response 0 Independent Variable(s) Examples any two categories, any binomial or binary variable a) Success-failure, Gender (Male-female), mortality, presence-absence, pass-fail, etc. The results of a simple linear regression is a slope and intercept which will produce a predicted value which ranges from 0 to 1 over most of the range of X This b" can be interpreted as a probability of obtaining a 1 per unit of X, and the predicted value is the probability of obtaining a 1 at some particular value of X. Problems with regression on indicator variables 1) Nonnormal errors : given that %3 = Y3 "! "" X3 , then When Y3 = 1, then When Y3 = 0, then 2) Nonconstant errors Let P(Y3 =1) = 13 and P(Y3 =0) = 1 13 then E(Y3 ) = 1(13 ) + 0(1 13 ) = 13 = "! "" X3 2 and 5]3 = E[Y3 E(Y3 )]2 = (1 13 )2 13 + (0 13 )2 (1 13 ) %3 = 1 "! "" X3 %3 = "! "" X3 = 13 (1 13 ) = E(Y3 )(1 E(Y3 )) finally, Var(%3 ) = Var(Y3 ), since %3 = Y3 13 and 13 is a constant 2 so 5%3 = 13 (1 13 ) = E(Y3 )(1 E(Y3 )) = ("! "" X3 )(1 "! "" X3 ) and the variance is a function of X3 3) Constraints on the response function If the function is fitted with a line, at some point the predicted value will be <0 or >1. As a probability, the true value must be between 0 and 1, so we must place some restraint on the predicted value. So we would like to find a function which solves some of these problems, we might also expect a curve instead of a simple linear and we would like a curve that can from go 0 to 1 (asymptotically) Several sigmoid possibilities have been considered, especially a) Logistic (symmetric) b) cumulative normal distribution (Probit analysis) This version of the logistic has several advantages, E(Y) = exp("! +"" X3 ) 1+exp("! +"" X3 ) particularly that it can be readily linearized by the transformation 1 1w = log/ 11 This is called a LOGIT transformation, and 1w is called a logit mean response. We can then fit w 13 = b! + b" X3 and we should closely approximate the logistic. The logistic can also be fitted directly with nonlinear techniques. A similar, but more difficult and less flexible, transformation exists for the cumulative normal distribution, and is called a PROBIT transformation Weighting to improve variance : the logit only linearizes the logistic function, it does not cure the nonhomogeneous variance problem The logit, 1 1w = log/ 11 is estimated by p pw3 = log/ 13p3 The variance of p3 is Var(pw3 ) = 1 n3 13 (113 ) which is estimated by, spw3 = 1 n3 p3 (1p3 ) we could therefore weight by w3 = n3 p3 (1 p3 ) in order to homogenize the variance. Notes: 1) logits are readily extendible to multiple regression. 2) Logistic regression has many applications. One common application in the biological sciences is the calculation of the dose needed to cause mortality. However, small doses cause small mortalities and large doses cause large mortalities. We therefore calculate an LD&! , which is the lethal dose for 50% mortality". for example, given the equation below ^w 13 = b! + b" X3 = -2.64 + 0.673*dose the LD50 is given by 50 ^w 1&! = log/ 150 = 0 0 = -2.64 + 0.673*dose&! dose&! = 2.64 0.673 = 3.923, or a dose of about 4
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LSU - STAT - 7034
EXST7034 : Regression Techniques Logistic regressionGeaghan Page 1Simple linear regression on an indicator variable a precursor to logistic regression Basically it is a simple linear regression where the dependent variable has a value of either
LSU - STAT - 7034
Statistical Techniques IIEXST7015Logistic Regression13a_LogisticReg 1Regression on an indicator variableWhat is an indicator variable? It is a variable with either the value 0 or 1.When we get to ANOVA we will see that class variables (categ
LSU - STAT - 7034
EXST7034 Regression Techniques Assignment 1Fall 2005 Page 1EXST7034 : Regression TechniquesHOMEWORK ASSIGNMENTS : General Information PC/NT Workstations are available in room 11 and room 48, both in the basement of the Ag. Admin. Building. Clas
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 1Fall 2005 Answer sheetGeaghan Page 1The SAS program I used to obtain the analyses for my answers is given below.dm'log;clear;output;clear'; *; * EXST7034 Homework Example 1 *; * Problem from Neter, Was
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 2Fall 2004Geaghan Page 1HOMEWORK ASSIGNMENT 2Assigned: September 20, 2005 Due: September 27 or 29, 200510 Points 1 point each day lateA) Complete the following questions using the values from probl
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 2Fall 2005 Answer sheetGeaghan Page 9The SAS program I used to obtain the analyses for my answers is given below.dm'log;clear;output;clear'; *; * EXST7034 Homework Example 1 *; * Problem from Neter, Was
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 2Fall 2005Geaghan Page 1HOMEWORK ASSIGNMENT 3Assigned: October 13, 2005 Due: October 20, 200510 Points 1 point each day lateComplete the following questions from your textbook. The problems come fr
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 3Fall 2005 Answer sheetGeaghan Page 17The SAS program I used to obtain the analyses for my answers is given below.*; * EXST7034 Homework Example **; * Applied Linear Statistical Models, 5th Edition, 200
LSU - STAT - 7034
EXST7034 Regression TechniquesFall 2005 GeaghanAssigned: October 20, 2005 Due: October 27, 200510 Points 1 point each day lateHOMEWORK ASSIGNMENT 4Complete the following questions from your textbook. The problems come from the &quot;Patient sati
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 4Fall 2005 Answer sheetGeaghan Page 24proc GLM data=Satisfaction; TITLE2 'Analysis with GLM'; MODEL Y=X2 X1 X3; RUN; proc REG data=Satisfaction; TITLE2 'Analysis with REG'; MODEL Y=X1 X2 X3 / vif stb PCO
LSU - STAT - 7034
EXST7034 Regression TechniquesHOMEWORK ASSIGNMENT 5Fall 2005Assigned: October 27, 2005 Due: November 3, 200510 Points 1 point each day lateSteroid use problem from chapter 8. The data is in dataset &quot;http:/www.stat.lsu.edu/EXSTWeb/statlab/dat
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 5Fall 2005 Answer sheetGeaghan Page 24The SAS program I used to obtain the analyses for my answers is given below.dm'log;clear;output;clear'; options nodate nocenter nonumber ps=512 ls=99 nolabel; ODS H
LSU - STAT - 7034
EXST7034 Regression TechniquesHOMEWORK ASSIGNMENT 6Fall 2003Assigned: November 3, 2005 Due: November 10, 200520 Points 1 point each day lateAll data is in &quot;http:/www.stat.lsu.edu/EXSTWeb/statlab/datasets/KNNLdata/&quot;. Complete the following qu
LSU - STAT - 7034
EXST7034 Regression Techniques Homework 6Fall 2005 Answer sheetGeaghan Page 31The program for the following sections follows.dm'log;clear;output;clear'; *; * EXST7034 Homework Example 1 **; * Problem from Neter, Wasserman &amp; Kuttner 1989, #2.1
LSU - STAT - 7034
EXST7034 Regression TechniquesHOMEWORK ASSIGNMENT 7Fall 2003Assigned: December 1, 2005 Due: December 8, 200510 Points 1 point each day lateAll data is in &quot;http:/www.stat.lsu.edu/EXSTWeb/statlab/datasets/KNNLdata/&quot;. Do the car purchase exampl
LSU - STAT - 3201
EXST3201 Background material From the textbook The Statistical SleuthPage 1Mean [20]: In your text the word mean denotes a population mean () while the work average denotes a sample average (Y). Variance [20]: The variance is a measure of the di
LSU - STAT - 3201
An Introduction to SAS Programming SAS programs consists of two major type of steps The DATA step used to create or modify a SAS dataset [Contents &gt; SAS Products &gt; Base SAS &gt; SAS Language concepts &gt; Data Step Concepts] SAS dataset a file containin
LSU - STAT - 3201
EXST3201 Mousefeed01Page 13 /* 4 Examine differences among the following 6 treatments 5 N/N85 fed normally before weaning and 85 kcal/wk after 6 N/R40 fed normally before weaning and 40 kcal/wk after 7 N/R50 fed normally before weaning and 50 kc
LSU - STAT - 3201
EXST3201 Chapter 5 Analysis of Variance [Chapter 5]GeaghanFall 2005: Page 1Testing between two samples is readily done with the two-sample t-test. In this situation we compare two groups (also referred to as classes, categories, treatments or i
LSU - STAT - 3201
EXST3201 Mousefeed02Page 11 /* 2 Examine differences among the following 6 treatments 3 N/N85 fed normally before weaning and 85 kcal/wk after 4 N/R40 fed normally before weaning and 40 kcal/wk after 5 N/R50 fed normally before weaning and 50 kc
LSU - STAT - 3201
EXST3201 Anatomy of a SAS program*; * The initial part of the program will *; * often have some comments. *; * - *; * Little boxes and lines are a nice *; * way to isolate these comments and *; * make them stand out. *; * - *; * For this box a comm
LSU - STAT - 3201
EXST3201 Chapter 5 Analysis of Variance [Chapter 5, part 2]GeaghanFall 2005: Page 1A second case of analysis of variance, the Dr. Spock conspiracy trail. This case is an observational study, so the data does not come from a planned experiment,
LSU - STAT - 3201
EXST3201 SpockTrial01aPage 11 /* 2 Fit an analysis of variance to determine if the jury for 3 spock trial was unusually low in the number of women. 4 */ 5 6 /* 7 SAS applications of note: 8 By statement with NOTSORTED 9 use of if statement to cr
LSU - STAT - 3201
EXST3201 Chapter 5GeaghanFall 2005: Page 1The text describes the analysis of variance in terms of the extra sum of squares principle. This is a useful concept with many applications, and will be demonstrated on two applications to the Spock tri
LSU - STAT - 3201
EXST3201 Chapter 6 Linear combinationsGeaghanFall 2005: Page 1A linear combination consists of a series of variables multiplied by constants. For a series of k variables the linear combination could be expressed as follows. Generic linear combi
LSU - STAT - 3201
EXST3201 Chapter 6GeaghanFall 2005: Page 1Tests based on the t-test and Multiple range tests One of the strengths of contrasts is that they should, in general, be made a priori. This means that the investigator is not conducting a wide search f
LSU - STAT - 3201
EXST3201 Mousefeed03bPage 1Below are Tukey adjusted pairwise comparisons done in PROC MIXED with range tests output from Saxtons macro. options ps=512 ls=88; proc mixed data=MouseDiet cl covtest; Title2 'Analysis of Variance with PROC MIXED'; cl
LSU - STAT - 3201
Statistical Analysis II EXST3201Simple Linear Regression03a_SLR 1The objectiveGiven points plotted on two coordinates, Y and X, find the best line to fit the data.Y - the dependent variable35302520012345678910X
LSU - STAT - 3201
EXST3201 Chapter 8aGeaghanFall 2005: Page 1Chapter 8 (More on Assumptions for the Simple Linear Regression) Chapter 8 covers the assumptions behind the SLR, and some alternative models that can be used. One of those alternatives involves the us
LSU - STAT - 3201
EXST3201 Chapter 8bGeaghanFall 2005: Page 1Chapter 8 (More on Assumptions for the Simple Linear Regression) Your textbook considers the following assumptions: Linearity This is not something I usually consider an explicit assumption, but obvio
LSU - STAT - 3201
EXST3201 Chapter 8cGeaghanFall 2005: Page 1Chapter 8 (A little more on Assumptions for the Simple Linear Regression) Linearity assumption the best way to determine an appropriate model is to examine the literature for a theoretical model, or t
LSU - STAT - 3201
EXST3201 : Statistical Analysis II Spring 2005 Multiple Regression Extra Sum of Squares 37 38 39 40 41 42 43 44 PROC REG MODEL MODEL MODEL MODEL MODEL MODEL MODEL DATA=ONE; Y = X1; Y = X2; Y = X3; Y = X1 X2 Y = X1 X3 Y = X2 X3 Y = X1 X2 TITLE2 'Sub
LSU - STAT - 3201
EXST3201 Chapter 9a Chapter 9 : Multiple RegressionGeaghanFall 2005: Page 1The first example of multiple regression is a designed experiment. The experiment involves the development of flowers on Meadowfoam a small cultivated plant used for its
LSU - STAT - 3201
EXST3201 Chapter 9bGeaghanFall 2005: Page 1Interpretation of regression coefficients: For the simple linear regression we know that the units of the intercept are the same as the units on the variable Y. The slope has units of Y units per X uni
LSU - STAT - 3201
EXST3201 Chapter 9cGeaghanFall 2005: Page 11 *; 2 * Brain size of selected mammals. *; 3 * Biologists are interested in the effect of brain *; 4 * size on variable slike gestation and litter size *; 5 *; 6 7 dm'log;clear;output;clear'; 8 option
LSU - STAT - 3201
EXST3201 Meadowfoam021 2 3 4 5 6 7 8 9 10 10GeaghanFall 2005: Page 1*; * The effect of light on Meadowfoam flowering. *; * Results of an experiment where the effedt of six *; * levels of light intensity and the timing of the *; * light treatm
LSU - STAT - 3201
EXST3201 WingSize01GeaghanFall 2005: Page 1This problem has elements of a two-way analysis of variance, or 2 x 2 factorial arrangements, of fruit fly sex and continent of residence. In addition to the factorial, there is a quantitative variabl
LSU - STAT - 3201
EXST3201 DummyVariable01GeaghanFall 2005: Page 1In Europe the fruit fly (Drosophila subovscura) has long been known to display a &quot;cline&quot;, that is a trend of increasing wing size with latitude. The fly was accidentally introduced to North Ameri
LSU - STAT - 3201
EXST3201 Multicolinearity Multicolinearity and singularityGeaghanFall 2005: Page 1With a perfect correlation an infinite number of models can be obtained. In practice, most software will bomb or detect the problem. Sample problem (all perfectly
LSU - STAT - 3201
EXST3201 Chapter 10aGeaghanFall 2005: Page 1Chapter 10 : Inferential tools for Multiple Regression A note on regression analysis in SAS In SAS, regression can be done in PROC REG, PROC GLM, PROC MIXED and numerous other specialty procedures. PR
LSU - STAT - 3201
EXST3201 Chapter 11a Chapter 11 : Model checking and refinementGeaghanFall 2005: Page 1This chapter is primarily concerned with diagnostics for individual observations. Previously, we have been concerned primarily with evaluating the model (ANO
LSU - STAT - 3201
EXST3201 Chapter 11b Chapter 11 : Model checking and refinementGeaghanFall 2005: Page 1An example: Blood-brain barrier study on rats This study investigates the permeability of the blood-brain barrier to medication. Rats were given cells that w
LSU - STAT - 3201
EXST7034 : Regression Techniques Multiple RegressionDiagnostic variables and criteriaGeaghan Page 1Criteria for the interpretation of selected statistics from the SAS output A) General regression diagnostics n 1 2 1) Adjusted R2 : Radj = 1 n p
LSU - STAT - 3201
EXST3201 KentuckyDerby01 Homework assignment 8.GeaghanFall 2005: Page 11 *; 2 * Speed of Kentucky Derby winner and track conditions *; 3 * for the years 1896 to 2000 *; 4 **; 5 6 dm'log;clear;output;clear'; 7 options nodate nocenter nonumber p
LSU - STAT - 3201
EXST3201 Chapter 12a Chapter 12 : Variable selectionGeaghanFall 2005: Page 1An example: State SAT scores In 1982 there was concern for scores of the Scholastic Aptitude Test (SAT) scores that varied greatly between states. Researchers decided
LSU - STAT - 3201
EXST3201 Chapter 13a Chapter 13 : Experimental designGeaghanFall 2005: Page 1Linear Models Yij = + i + ij the basic completely randomized design, or one-way ANOVA d.f. Source Treatments t 1 t(n 1) Error Error structure (random effects) Ne
LSU - STAT - 3201
EXST3201 Chapter 13bGeaghanFall 2005: Page 1Chapter 13 : The Meadowfoam experiment, a CRD factorial Linear Models Yij = + 1i + 2 j + 1 2ij + ijk This is a completely randomized design with a 2 by 6 factorial treatment arrangement (two-way
LSU - STAT - 3201
EXST7005 - Statistical Techniques I23a ANOVA Factorial.prz - 1-6Statistical Techniques IEXST7005The Factorial Treatment ArrangementAlso known as &quot;two-way&quot; ANOVAThis analysis has two (or more) Treatments, for example treatment A with two leve
LSU - STAT - 3201
EXST3201 Chapter 13d Chapter 13 a few final notesGeaghanFall 2005: Page 1The textbook has a good image demonstrating types of additivity. Make sure you understand this concept and how to test it.Discussion points from the text Randomized blo
LSU - STAT - 3201
EXST3201 Chapter 14aGeaghanFall 2005: Page 1Chapter 14 : Multifactor studies without replication Linear Models Yij = + i + j + ij This is a randomized block design with no replication beyond the treatment by block interaction. The treatmen
LSU - STAT - 3201
EXST3201 Chapter 14bGeaghanFall 2005: Page 1Chapter 14 : Multifactor studies without replication Effects of Ozone with Sulfur Dioxide and Water Stress on Soybean Yield This study involved two different soybean cultivars. The 30 possible combina
LSU - STAT - 3201
EXST3201 Assignment 2Page 1The objective of this assignment is continuing practice with the SAS software. In addition to the SAS programming components used for assignment 1, this assignment will require 1) input of an external data set, 2) start
LSU - STAT - 3201
EXST3201 Assignment 3Page 1The objective of this assignment is continuing practice with the SAS software. For this assignment the SAS programming will require; 1) input of an external data set, (ex0524.csv). Store this dataset in C:|\TEMP\. 2) St
LSU - STAT - 3201
EXST3201 Assignment 4Page 1The objective of this assignment is to apply some of the post-ANOVA applications covered this week. On assignment 2, the Tyrannosaurus Rex analysis, the bones listed as Bone1 through BONE12 are the following:Indication
LSU - STAT - 3201
EXST3201 Assignment 5Page 1The objective of this assignment is to run a regression analysis. We have not covered SAS regression output yet, so we will fit an initial program today and embellish this program next week. Therefore, make sure you sav
LSU - STAT - 3201
EXST3201 Assignment 6Page 1The objective of this assignment is to run a regression analysis and to do some selected tests of hypothesis. You should already have a program that does the following. a) Inputs 3 variables (DATE INTERVAL DURATION) fro
LSU - STAT - 3201
EXST3201 Assignment 7Page 1The objective of this assignment is to run a MULTIPLE regression analysis with selected diagnostics. I have modified the data set by adding the city to the observations. You may use the following input statements.data
LSU - STAT - 3201
EXST3201 Assignment 8Page 1The objective of this assignment is to run a MULTIPLE regression with linear and quadratic terms and interaction. You may use the following input statements. Note that if you use power terms or interactions with PROC RE
LSU - STAT - 3201
EXST3201 Assignment 9Page 1Today, we have a bit of a challenge. At a minimum you should fit an Analysis of Covariance to the data (description on the next page). The dataset is ex0920.csv. You may use PROC GLM or PROC REG. If you use PROC REG you
LSU - STAT - 3201
EXST3201 Assignment 10Page 1The dataset for today is ex1123.csv. I recommend you use PROC REG. The data step is as follows. data AirPollution; length city \$ 18; infile input1 missover DSD dlm=&quot;,&quot; firstobs=2; input CITY \$ MORT PRECIP EDUC NONWHITE
LSU - STAT - 3201
EXST3201 Assignment 11Page 1-The dataset for today is ex1320.csv. I recommend you use PROC MIXED or PROC GLM (or both) for this example. There are no random effects, so the problem is appropriate for either. data ACTSCORES; infile input1 missover