Tobit and Selection Models HISHAM ABOU-TALEB R3 basics course - 2014.06.02.

Slides:

Advertisements

Similar presentations

Chapter 3 Examining Relationships Lindsey Van Cleave AP Statistics September 24, 2006.

Advertisements

Qualitative and Limited Dependent Variable Models Chapter 18.

Economics 20 - Prof. Anderson1 Limited Dependent Variables P(y = 1|x) = G(  0 + x  ) y* =  0 + x  + u, y = max(0,y*)

Managerial Economics in a Global Economy

Geometric Representation of Regression. ‘Multipurpose’ Dataset from class website Attitude towards job –Higher scores indicate more unfavorable attitude.

Kin 304 Regression Linear Regression Least Sum of Squares

Statistics Measures of Regression and Prediction Intervals.

MA-250 Probability and Statistics

LINEAR REGRESSION: Evaluating Regression Models. Overview Standard Error of the Estimate Goodness of Fit Coefficient of Determination Regression Coefficients.

GRA 6020 Multivariate Statistics The regression model OLS Regression Ulf H. Olsson Professor of Statistics.

1 BA 275 Quantitative Business Methods Simple Linear Regression Introduction Case Study: Housing Prices Agenda.

C82MCP Diploma Statistics School of Psychology University of Nottingham 1 Linear Regression and Linear Prediction Predicting the score on one variable.

Simple Linear Regression Analysis

Relationships Among Variables

Lecture 5 Correlation and Regression

Correlation and Linear Regression

Introduction to Linear Regression and Correlation Analysis

Regression Analysis Regression analysis is a statistical technique that is very useful for exploring the relationships between two or more variables (one.

Chapter 11 Simple Regression

Correlation and Linear Regression. Evaluating Relations Between Interval Level Variables Up to now you have learned to evaluate differences between the.

Correlation is a statistical technique that describes the degree of relationship between two variables when you have bivariate data. A bivariate distribution.

McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 13 Linear Regression and Correlation.

Regression Regression relationship = trend + scatter

Univariate Linear Regression Problem Model: Y=  0 +  1 X+  Test: H 0 : β 1 =0. Alternative: H 1 : β 1 >0. The distribution of Y is normal under both.

Issues in Estimation Data Generating Process:

1 Tobit Analysis of Vehicle Accident Rates on Interstate Highways Panagiotis Ch. Anastasopoulos, Andrew Tarko, and Fred Mannering.

11/23/2015Slide 1 Using a combination of tables and plots from SPSS plus spreadsheets from Excel, we will show the linkage between correlation and linear.

STA291 Statistical Methods Lecture LINEar Association o r measures “closeness” of data to the “best” line. What line is that? And best in what terms.

7.4 DV’s and Groups Often it is desirous to know if two different groups follow the same or different regression functions -One way to test this is to.

Mixed Cost Analysis 3 Fixed And Variable Costs Cost Behavior – Mixed Costs y x Cost Activity level y x Cost Activity level a y x Cost Activity level.

Correlation They go together like salt and pepper… like oil and vinegar… like bread and butter… etc.

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Simple Linear Regression Analysis Chapter 13.

Nonrandom Sampling and Tobit Models ECON 721. Different Types of Sampling Random sampling Censored sampling Truncated sampling Nonrandom –Exogenous stratified.

Statistics.  Percentiles ◦ Divides a data set into 100 equal parts  A score of 1700 on the SAT puts students in the 72 nd Percentile. ◦ 72% score 1700.

©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin Linear Regression and Correlation Chapter 13.

Statistics 350 Lecture 2. Today Last Day: Section Today: Section 1.6 Homework #1: Chapter 1 Problems (page 33-38): 2, 5, 6, 7, 22, 26, 33, 34,

Introduction Many problems in Engineering, Management, Health Sciences and other Sciences involve exploring the relationships between two or more variables.

Chapter 4. The Normality Assumption: CLassical Normal Linear Regression Model (CNLRM)

Simple Linear Regression In many scientific investigations, one is interested to find how something is related with something else. For example the distance.

The simple linear regression model and parameter estimation

Testing Happiness Hypothesis among the Elderly Alejandro Cid () Daniel Ferrés () Máximo Rossi ( ) July 2007  Universidad de Montevideo  

Objectives Fit scatter plot data using linear models.

Multiple Imputation using SOLAS for Missing Data Analysis

Regression Chapter 6 I Introduction to Regression

REGRESSION DIAGNOSTIC II: HETEROSCEDASTICITY

Kin 304 Regression Linear Regression Least Sum of Squares

Chapter 5 STATISTICS (PART 4).

SIMPLE LINEAR REGRESSION MODEL

Chapter 3: TWO-VARIABLE REGRESSION MODEL: The problem of Estimation

BPK 304W Regression Linear Regression Least Sum of Squares

Charles University Charles University STAKAN III

Limited Dependent Variable Models and Sample Selection Corrections

1) A residual: a) is the amount of variation explained by the LSRL of y on x b) is how much an observed y-value differs from a predicted y-value c) predicts.

Tetiana Ianevych and Veronika Serhiienko

I271B Quantitative Methods

2-7 Curve Fitting with Linear Models Holt Algebra 2.

Introduction to microeconometrics

Simple Linear Regression

Two-Variable Regression Model: The Problem of Estimation

Linear regression Fitting a straight line to observations.

I271b Quantitative Methods

STA 291 Summer 2008 Lecture 23 Dustin Lueker.

LIMITED DEPENDENT VARIABLE REGRESSION MODELS

SIMPLE LINEAR REGRESSION

Section 6.2 Prediction.

Linear Regression Summer School IFPRI

Review I am examining differences in the mean between groups How many independent variables? OneMore than one How many groups? Two More than two ?? ?

STA 291 Spring 2008 Lecture 23 Dustin Lueker.

Linear Regression and Correlation

REVIEW Course Review.

Presentation transcript:

Tobit and Selection Models HISHAM ABOU-TALEB R3 basics course

Tobit Model a censored regression The TOBIT model is a statistical model proposed by James Tobin (1958). It also called a censored regression model. It is designed to estimate linear relationships between variables when there is either left- or right- censoring in the dependent variable (also known as censoring from below and above, respectively).

Tobit Model Censoring from aboveCensoring from above takes place when cases with a value at or above some threshold, all take on the value of the threshold. The true value might be equal to the threshold, but it might also be higher. In the case of censoring from below, values those that fall at or below some threshold are censored.

Type 1 Tobit Simple Tobit model where the outcome variable is observed only if it is above or below a given threshold. Censoring can be at a value yL, different from zero Example: Restricting speedometer readings to 85 mph. So, if we want to predict a vehicle's top- speed from a combination of horse-power and engine size, you would get a reading no higher than 85, regardless of how fast the vehicle was really traveling.

Type 1 Tobit N < u <- rnorm(N) x < rnorm(N) ystar <- 1 + x + u y 0) hist(y) ols <- lm(y ~ x) summary(ols) library(AER) tobit <- tobit(y ~ x,left=0,right=Inf,dist = "gaussian")

Type 2 Tobit Heckit modelIt is also known as Heckit model The outcome y2 is observed only if y1 is equal to 0. y1 a binary variable which may be correlated with the error term of y2, resulting in endogenous selection process.

Type 2 Tobit N < u <- rnorm(N) v <- rnorm(N) x < rnorm(N) z <- 1 + rnorm(N) d 0) ystar <- 1 + x + u y <- ystar*(d == 1) hist(y) ols <- lm(y ~ x) summary(ols)

Type 2 Tobit Also we can use heckit() and selection() in sampleSelection package library(sampleSelection) heckit.ml <- heckit(selection = d ~ x + z, outcome = y ~ x, method = "ml") summary(heckit.ml) heckit.2step <- heckit(selection = d ~ x + z, outcome = y ~ x, method = "2step") summary(heckit.2step)

Truncation Truncated regression is used to model dependent variables for which some of the observations are not included in the analysis because of the value of the dependent variable. We can use the truncreg package in R for this analysis Example: students are required to have a minimum score of 40 to pass the exam. Thus, the sample is truncated at an achievement score of 40. Doubly truncated data analysis (DTDA package)