disc choice5.tex; April 11, ffl See: King - Unifying Political Methodology ffl See: King/Tomz/Wittenberg (1998, APSA Meeting). ffl See: Alvarez
|
|
- Lesley Willis
- 5 years ago
- Views:
Transcription
1 disc choice5.tex; April 11, Lecture Notes on Discrete Choice Models Copyright, April 11, 2001 Jonathan Nagler 1 Topics 1. Review the Latent Varible Setup For Binary Choice ffl Logit ffl Likelihood for Logit ffl Probabilities 2. RUM: The Random Utility Model formulation of choice. ffl Flexible ffl A strong (or weak) model of behavior. 3. Multinomial Logit ffl Likelihood ffl Probabilities 4. Conditional Logit ffl a More General Systemic Component of Model ffl Probabilities are Calculated the same as MNL 5. Measuring The Effects of Changes in X: ffl Analagous to OLS
2 disc choice5.tex; April 11, ffl See: King - Unifying Political Methodology ffl See: King/Tomz/Wittenberg (1998, APSA Meeting). ffl See: Alvarez and Nagler 1995 ( Perot "; Table 4), first differences 6. Measuring the Effects of Changes in the Choices ffl See: Alvarez and Nagler 1998 ( Collide"; Table 5 - moving Labour Party). 7. Goodness of Fit ffl Percent correctly predicted in 2-choice case. ffl Baseline Prediction in 2-choice case. ffl Percent Correctly predicted in J-choice case: Baseline Prediction Classification Schemes 8. Independence of Irrelevant Alternatives (IIA) ffl What is IIA ffl IIA does not aggregate ffl McFadden test for IIA 9. Multinomial Probit (MNP) ffl Does not impose IIA. ffl Need to put restrictions on ±. ffl Estimation via: Gauss, Gaussx, Limdep ffl Beyond 5 choices?
3 disc choice5.tex; April 11, Some Equivalencies of Logit Models 11. Scobit ffl MNL can be used to recover reduced form CL estimates. ffl MNL is equivalent to Binary Logit (under IIA). ffl What if basic assumption of the shape of the response curve is wrong? 12. Heteroscedastic Probit 13. Selection Bias ffl Heckman ffl Dubin and Rivers
4 disc choice5.tex; April 11, Latent Variable Setup: Binary Probit/Logit y Λ = fi 0 x + ffl (1) y = 1 if y Λ > 0 (2) y = 0 if y Λ» 0 (3) Now assume F is the cumulative distribution for ffl. Prob(y = 1) = Prob(y Λ > 0) (4) = Prob(fi 0 x + ffl > 0) = Prob(ffl > fi 0 x) = 1 Prob(ffl < fi 0 x) = 1 F ( fi 0 x) (5) If F is symmetric about 0, Prob(y = 1) = 1 F ( fi 0 x) = F (fi 0 x) (6) If F is the logistic distribution this gives us logit, if F is the cumulative normal distribution we have probit. In either case, logit or probit would recover consistent estimates of the parameter fi. Logistic distribution looks like: F (x) = e x (7)
5 disc choice5.tex; April 11, So, if F is logistic: Prob(y = 1) = F (fi 0 x) = = e fi 0 x e fi 0 x 1 + e fi 0 x So, if we could estimate fi, then we could compute the quantity of interest (P ). We use maximum likelihood to compute fi: we want to find fi to maximize: Pr(Y j fi; X) In the simple case, we have two possibilities: y i = 1 or y i = 0. Pr(y 1 ;y 2 ; ::::; y N j fi) = Y yi=1 Pr(Y i = 1 j fi; X) Y Pr(Y i = 0 j fi; X) y i =0
6 disc choice5.tex; April 11, Wework with something similar to the above: the likelihood function (L). The following assumes F is symettric, and substitutes F for Pr(Y i = 1): L = Y yi=1 F (X i fi j fi) Y y i =0 (1 F (X i fi j fi)) = Y F (X i fi j fi) y i Y (1 F (Xi fi j fi)) 1 y i We always work with log(l) - or the log-likelihood function. LL = X y i ln(f (X i fi)) + X (1 y i )ln((1 F (X i fi))) So, we take the first derivatives of the above expression with respect to fi, set them equal to 0, and solve for ^fi.
7 disc choice5.tex; April 11, Random Utility Models (RUM) Assume the i th individual's utility of the j th choice is given as: U ij = V ij + ffl ij (8) where V ij is a systemic component of utility and ffl ij is a stochastic component of utility. Assume that the i th individual chooses choice j iff: U ij > U ik 8 k 6= j (9) Notice that ffl ij is subscripted by i and j. We have one disturbance per respondent per choice. Simple setup of V ij : V ij = fi j X ij (10) (11) This model is very flexible: it allows for more than 2 choices. The model is a weak or strong model of behavior.
8 disc choice5.tex; April 11, RUM Example 1: Multinomial Logit V ij = ψ j X i (12) V ij = ψ j0 + ψ j1 pid i + ψ j2 educ i + ψ j3 ideology i (13) V i1 = ψ 10 + ψ 11 pid i + ψ 12 educ i + ψ 13 ideology i V i2 = ψ 20 + ψ 21 pid i + ψ 22 educ i + ψ 23 ideology i V i3 = ψ 30 + ψ 31 pid i + ψ 32 educ i + ψ 33 ideology i So: U i1 = ψ 10 + ψ 11 pid i + ψ 12 educ i + ψ 13 ideology i + ffl i1 U i2 = ψ 20 + ψ 21 pid i + ψ 22 educ i + ψ 23 ideology i + ffl i2 U i3 = ψ 30 + ψ 31 pid i + ψ 32 educ i + ψ 33 ideology i + ffl i3 ffl are iid, Type I Extreme Value. P i1 = Pr[(U i1 > U i2 ) & (U i1 > U i3 )] = Pr[(V i1 + " i1 > V i2 + " i2 ) & (V i1 + " i1 > V i3 + " i3 )] = Pr[(" i2 " i1 < V i1 V i2 ) & (" i3 " i1 < V i1 V i3 )] Notice: ψ is indexed by j.
9 disc choice5.tex; April 11, Normalization of One Set of ψ's U i1 = ψ 1 A i + " i1 U i2 = ψ 2 A i + " i2 U i3 = ψ 3 A i + " i3 P i1 = Pr[(U i1 > U i2 ) & (U i1 > U i3 )] = Pr[(ψ 1 A i + " i1 > ψ 2 A i + " i2 ) & (ψ 1 A i + " i1 > ψ 3 A i + " i3 )] = Pr[(" i2 " i1 < (ψ 1 ψ 2 )A i ) & (" i3 " i1 < (ψ 1 ψ 3 )A i )] P i2 = Pr[(" i1 " i2 < (ψ 2 ψ 1 )A i ) & (" i3 " i2 < (ψ 2 ψ 3 )A i )] P i3 = Pr[(" i1 " i3 < (ψ 3 ψ 1 )A i ) & (" i2 " i3 < (ψ 3 ψ 2 )A i )] 3 Quantities: Ψ 1 Ψ 2 = X Ψ 1 Ψ 3 = Y Ψ2 Ψ 3 = Z But: Z = Y X
10 disc choice5.tex; April 11, Example: Ψ 1 = 7 Ψ 2 = 4 Ψ 3 = 0 Yields: Ψ 1 Ψ 2 = 3 Ψ 1 Ψ 3 = 7 Ψ2 Ψ 3 = 4 Same Result if: Ψ 1 = 24 Ψ 2 = 21 Ψ 3 = 17 Yields: Ψ 1 Ψ 2 = 3 Ψ 1 Ψ 3 = 7 Ψ2 Ψ 3 = 4
11 disc choice5.tex; April 11, Probabilities: We do not prove the following here; but it is true. P ij = e V ij PJ k=1 ev ik (14) Simple 2-Choice Case: Pr(Y i = 1) = = This looks like binary logit: F (x) = = = = e fi 0 1 X i e fi 0 1 X i e fi 0 1 X i + e fi 0 2 X i e fi 0 1 X i e x e x 1 e x + 1 e x e x e x + 1 (15) (16)
12 disc choice5.tex; April 11, Table 2: Multinomial Logit and Binomial Logit Estimates British Election (Alvarez and Nagler 1998) Conservative/Alliance Labour/Alliance MNL BL MNL BL Intercept -4.33* -4.40* 4.55* 5.26* (.74) (.76) (.81) (.86) Defense.14*.17* -.17* -.19* (.03) (.03) (.03) (.03) Phillips Curve.08*.10* (.02) (.03) (.03) (.03) Taxation.13*.14* -.06** -.08* (.03) (.03) (.03) (.04) National..16*.16* -.16* -.20* (.03) (.03) (.03) (.03) Redist..07*.06* -.08* -.09* (.02) (.02) (.03) (.03) Crime.08*.08* (.03) (.03) (.02) (.02) Welfare.11*.12* -.11* -.10* (.02) (.02) (.03) (.03) South * -.45* (.16) (.17) (.21) (.22) Midlands (.17) (.17) (.21) (.21) North *.61* (.17) (.18) (.19) (.20) Wales * 1.46* (.35) (.36) (.31) (.33) Scot **.68*.61* (.25) (.26) (.25) (.26) Union *.37*.35* (.16) (.16) (.16) (.17) Public Employee (.15 (.15 (.16 (.16 Blue Collar *.80* (.15) (.16) (.17) (.17) Gender.29*.33* (.14) (.14) (.15) (.16) Age * -.24* (.05) (.05) (.05) (.05) Homeowner.31** * -52* (.18) (.18) (.17) (.17) Income.07*.07* * (.03) (.03) (.03) (.03) Education -.81* -.92* ** (.31) (.31) (.35) (.36) Inflation.28*.31* (.10) (.11) (.12) (.12) Taxes * (.06) (.07) (.07) (.07) Unempl..30* (.06) (.06) (.07) (.08) Number of Observations Log Likelihood Standard Errors in parenthesis. Λ indicates significance at 95% level; ΛΛ indicates significance at 90% level.
13 disc choice5.tex; April 11, Consider just a 2-choice comparison: U i1 = fi 0 1 X i + ffl i1 (17) U i2 = fi 0 2 X i + ffl i2 (18) Pr(U i2 > U i1 ) = Pr(fi 0 1 X i + ffl i1 < fi 0 2 X i + ffl i2 ) = Pr(ffl i1 ffl i2 < (fi 0 2 fi 0 1 )X i) (19) Back to latent variable model: Pr(Y i = 1) = Pr(u i < fi 0 X i ) (20) So: u i ß ffl i1 ffl i2 fi ß fi 2 fi 1 (21) If we assume ffl ij are independent, identically distributed with Type 1 Extreme Value distribution, then ffl i1 ffl i2 is logistically distributed. F (ffl ij ) = exp(e ffl ij ) (22) Assume fi 2 = 0. This is just a normalization, we could assume fi 2 = 17. The only thing that matters is U i1 U i2.
14 disc choice5.tex; April 11, Conditional Logit U ij = ψ 0 j A i + fi 0 X ij + ffl ij (23) where: U ij = utility of the i th respondent for the j th alternative. A i = characteristics of the i th respondent. X ij = characteristics of the j th alternative relative to the i th respondent. ψ j = a vector of parameters relating the characteristics of a respondent to the respondent's utility for the j th alternative. fi = a vector of parameters relating the relationship between the respondent and the alternative (X ij ) to the respondent's utility for the alternative. ffl ij = random disturbance for the i th respondent for the j th alternative; iid, Type I Extreme Value. Notice: ψ j varies across choices. Both conditional logit and multinomial logit models assume that the disturbances, ffl ij, are independent across alternatives.
15 disc choice5.tex; April 11, RUM Example 2: Conditional Logit V ij = fi 1 X ij + ψ j A i V ij = fi 1 issuedist ij + ψ j0 + ψ j1 pid i + ψ j2 educ i V i1 = fi 1 issuedist i1 + ψ 10 + ψ 11 pid i + ψ 12 educ i V i2 = fi 1 issuedist i2 + ψ 20 + ψ 21 pid i + ψ 22 educ i V i3 = fi 1 issuedist i3 + ψ 30 + ψ 31 pid i + ψ 32 educ i So: U i1 = fi 1 issuedist i1 + ψ 10 + ψ 11 pid i + ψ 12 educ i + ffl i1 U i2 = fi 1 issuedist i2 + ψ 20 + ψ 21 pid i + ψ 22 educ i + ffl i2 U i3 = fi 1 issuedist i3 + ψ 30 + ψ 31 pid i + ψ 32 educ i + ffl i3
16 disc choice5.tex; April 11, Table 4 Conditional Logit Estimates British Election Conservative/Alliance Labour/Alliance Defense a -.18* (.02) Phillips Curve -.11* (.02) Taxation -.16* (.02) National. -.18* (.02) Redist. -.08* (.02) Crime -.10* (.05) Welfare -.14* (.02) Intercept * (.69) (.75) South * (.17) (.21) Midlands -.29**.19 (.17) (.20) North * (.18) (.19 Wales * (.36) (.31) Scot * (.25) (.25) Union -.50*.37* (.16) (.16) Public Employee (.15) (.16) Blue Collar.11.70* (.15) (.16) Gender.28*.00 (.14) (.15) Age * (.05) (.05) Homeowner.37* -.54* (.18) (.16) Income.07* -.06 (.03) (.03) Education -.82* -.61** (.32) (.35) Inflation.28* -.03 (.10) (.11) Taxes (.07) (.07) Unempl..28* (.01 (.06) (.07) N 2131 Log Likelihood a The seven issues represent distance absolute value from the respondent tothe mean of the party position. Standard Errors in parenthesis. Λ indicates significance at 95% level; ΛΛ indicates significance at 90% level.
17 disc choice5.tex; April 11, Probabilities We do not prove the following here; but it is true. P ij = e fi0 X ij + ψj 0 A i P J X ik + ψ 0 k=1 efi0 k A i = e V ij P J k=1 ev ik Same probabilities as MNL. Just another form of MNL.
18 disc choice5.tex; April 11, Goodness of Fit, Predicted Values, Classification There is no R 2. Pseudo-R 2 "! even worse than R 2. Compute ^P ij. ^P ij! ^Y i Classification Rule (binomial): ^Y i = 1 if ^P i > :5 Percent Correctly Predicted: correct prediction": ^Yi = 1 and Y i = 1 or, ^Y i = 0 and Y i = 0. PCP = 100(# of Correct Predictions) N PMC = Percent in Modal Category
19 disc choice5.tex; April 11, PRE [Proportional Reduction in Error]: PRE = PCP PMC 1 PMC Example 1: PCP =.85 PMC =.80 Example 2: PRE = PCP =.75 PMC =.50 :85 :80 1 :80 = :05 :20 = :25 PRE = :75 :50 1 :50 = :25 :50 = :50 Classification Rule (multinomial): If you require ^P ij > :5 for ^y i = j, then you may not classify some observations. So: ^y i = j if ^Pij > ^P ik 8k 6= j.
20 disc choice5.tex; April 11, Unevenly Distributed Data: If the data has a very skewed distribution (90% 0's; 10% 1's), you may never predict 1 as an outcome. Common in multinomial cases where one case may be relatively rare. A Useful Table (hypothetical numbers): Pred Observed Cons Labour All d Total d Cons d Labour d Alliance Total This table has all the information (except uncertainty). We can see that we do not predict votes for Alliance very well.
21 disc choice5.tex; April 11, cpcp (Herron ) Problem: We treat ^P i = :51 and Y i = 1 the same as ^P i = :95 and Y i = 1. But, we should give more credit for the latter prediction: it is a `better' prediction. Solution: Expected PCP". epcp = 1 N X Yi=1 ^P i + X (1 ^P i ) 1 A Y i =0 Example: Y i ^Pi epcp = 1/3 ( ) =.6
22 disc choice5.tex; April 11, epcp - Multinomial epcp = 1 N NX JX ^Pij (y i == j) i=1 j=1 epcp = 1 3 X Yi=1 ^P i1 + X Yi=2 ( ^P i2 ) + X Yi=3( ^P i3 ) 1 A
23 disc choice5.tex; April 11, Computing Effects of Changes in Characteristics of a Respondent P ij = e fi0 X ij + ψj 0 A i P J X ik + ψ 0 k=1 efi0 k A i (24) Say: we want to know what happens if a i were to change to ~a i ; say a i were to increase by z units. [a i is a particular element of the vector A i.] 1. Compute : ~a i = a i + z 2. Compute: Vij ~ = fi 0 X ij + ψ ~ 0 j A i 3. Compute P ~ ij 4. Compute: Pij ~ ^P ij The last difference is the quantity of interest. We could also compute this for everyone in the sample, and then compute the mean of Pij ~ ^P ij ; and get the effect of all respondents changing their taste on characteristic a by z units.
24 disc choice5.tex; April 11, Table 4 (A/N AJPS) Effects of Economics, Issues, and Anger in the 1992 Election Probability of Voting For: Bush Clinton Perot Personal Finances Better Worse Difference National Economy Better Worse Difference Voter Ideology a Near Far Difference Minorities Assist No Assist Difference Abortion Pro-Life Pro-Choice Difference Term Limits For Against Difference Note: Table entries are the predicted probabilities of a hypothetical individual voting for Clinton, Bush or Perot based on different values of the row-variable. a Probabilities for each of the candidates in the voter-ideology row are based on the ideological distance between the voter and the particular candidate.
25 disc choice5.tex; April 11, Computing Effects of Changes in Characteristics of an Alternative ^P ij = e ^fi 0 X ij + ^ψ 0 j A i PJ k=1 e ^fi 0 X ik + ^ψ 0 k A i (25) We want to alter A i, and recompute ^P ij. Say: X ij = (resp i choice j ) (26) We want to know what happens if the j th choices `moves' z units to the right. 1. Set: g choicej = choice j + z 2. Compute: ~ Xij = (resp i g choicej ) 3. Compute: Vij ~ = fi ~ 0 Xij + ψ 0 j A i 4. Compute P ~ ij 5. Compute: Pij ~ ^P ij The last difference is the quantity of interest.
26 disc choice5.tex; April 11, Table 5 (A/N AJPS) Conditional Logit Estimates of Effect of Movement By the Labour Party +/- 1 Standard Deviation 2 - British Election Conservatives Labour Alliance Baseline Defense 1 ff ff Difference Phillips 1 ff ff Difference Taxation 1 ff ff Difference Nationalization 1 ff ff Difference All Issues 1 ff ff Difference Note: Estimated impact of the Labour party moving from one half a standard deviation to the left of its mean perceived position to one half a standard deviation to the right of its mean perceived position on each of seven issues. Column entries are estimated aggregate vote-shares.
Goals. PSCI6000 Maximum Likelihood Estimation Multiple Response Model 1. Multinomial Dependent Variable. Random Utility Model
Goals PSCI6000 Maximum Likelihood Estimation Multiple Response Model 1 Tetsuya Matsubayashi University of North Texas November 2, 2010 Random utility model Multinomial logit model Conditional logit model
More informationPOLI 7050 Spring 2008 February 27, 2008 Unordered Response Models I
POLI 7050 Spring 2008 February 27, 2008 Unordered Response Models I Introduction For the next couple weeks we ll be talking about unordered, polychotomous dependent variables. Examples include: Voter choice
More informationEconometrics Lecture 5: Limited Dependent Variable Models: Logit and Probit
Econometrics Lecture 5: Limited Dependent Variable Models: Logit and Probit R. G. Pierse 1 Introduction In lecture 5 of last semester s course, we looked at the reasons for including dichotomous variables
More informationGoals. PSCI6000 Maximum Likelihood Estimation Multiple Response Model 2. Recap: MNL. Recap: MNL
Goals PSCI6000 Maximum Likelihood Estimation Multiple Response Model 2 Tetsuya Matsubayashi University of North Texas November 9, 2010 Learn multiple responses models that do not require the assumption
More informationDiscrete Choice Models I
Discrete Choice Models I 1 Introduction A discrete choice model is one in which decision makers choose among a set of alternatives. 1 To fit within a discrete choice framework, the set of alternatives
More informationConsider Table 1 (Note connection to start-stop process).
Discrete-Time Data and Models Discretized duration data are still duration data! Consider Table 1 (Note connection to start-stop process). Table 1: Example of Discrete-Time Event History Data Case Event
More informationh=1 exp (X : J h=1 Even the direction of the e ect is not determined by jk. A simpler interpretation of j is given by the odds-ratio
Multivariate Response Models The response variable is unordered and takes more than two values. The term unordered refers to the fact that response 3 is not more favored than response 2. One choice from
More informationAdvanced Quantitative Methods: limited dependent variables
Advanced Quantitative Methods: Limited Dependent Variables I University College Dublin 2 April 2013 1 2 3 4 5 Outline Model Measurement levels 1 2 3 4 5 Components Model Measurement levels Two components
More informationMultiple regression: Categorical dependent variables
Multiple : Categorical Johan A. Elkink School of Politics & International Relations University College Dublin 28 November 2016 1 2 3 4 Outline 1 2 3 4 models models have a variable consisting of two categories.
More information13.1 Categorical Data and the Multinomial Experiment
Chapter 13 Categorical Data Analysis 13.1 Categorical Data and the Multinomial Experiment Recall Variable: (numerical) variable (i.e. # of students, temperature, height,). (non-numerical, categorical)
More informationLimited Dependent Variable Models II
Limited Dependent Variable Models II Fall 2008 Environmental Econometrics (GR03) LDV Fall 2008 1 / 15 Models with Multiple Choices The binary response model was dealing with a decision problem with two
More informationItem Response Theory for Conjoint Survey Experiments
Item Response Theory for Conjoint Survey Experiments Devin Caughey Hiroto Katsumata Teppei Yamamoto Massachusetts Institute of Technology PolMeth XXXV @ Brigham Young University July 21, 2018 Conjoint
More informationStat 642, Lecture notes for 04/12/05 96
Stat 642, Lecture notes for 04/12/05 96 Hosmer-Lemeshow Statistic The Hosmer-Lemeshow Statistic is another measure of lack of fit. Hosmer and Lemeshow recommend partitioning the observations into 10 equal
More informationChapter 11. Regression with a Binary Dependent Variable
Chapter 11 Regression with a Binary Dependent Variable 2 Regression with a Binary Dependent Variable (SW Chapter 11) So far the dependent variable (Y) has been continuous: district-wide average test score
More informationConducting Multivariate Analyses of Social, Economic, and Political Data
Conducting Multivariate Analyses of Social, Economic, and Political Data ICPSR Summer Program Concordia Workshops May 25-29, 2015 Dr. Harold D. Clarke University of Texas, Dallas hclarke@utdallas.edu Dr.
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 informationBinary Choice Models Probit & Logit. = 0 with Pr = 0 = 1. decision-making purchase of durable consumer products unemployment
BINARY CHOICE MODELS Y ( Y ) ( Y ) 1 with Pr = 1 = P = 0 with Pr = 0 = 1 P Examples: decision-making purchase of durable consumer products unemployment Estimation with OLS? Yi = Xiβ + εi Problems: nonsense
More informationBinary Dependent Variable. Regression with a
Beykent University Faculty of Business and Economics Department of Economics Econometrics II Yrd.Doç.Dr. Özgür Ömer Ersin Regression with a Binary Dependent Variable (SW Chapter 11) SW Ch. 11 1/59 Regression
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 informationOutline. The binary choice model. The multinomial choice model. Extensions of the basic choice model
Outline The binary choice model Illustration Specification of the binary choice model Interpreting the results of binary choice models ME output The multinomial choice model Illustration Specification
More informationThe Logit Model: Estimation, Testing and Interpretation
The Logit Model: Estimation, Testing and Interpretation Herman J. Bierens October 25, 2008 1 Introduction to maximum likelihood estimation 1.1 The likelihood function Consider a random sample Y 1,...,
More informationThe Causal Inference Problem and the Rubin Causal Model
The Causal Inference Problem and the Rubin Causal Model Lecture 2 Rebecca B. Morton NYU Exp Class Lectures R B Morton (NYU) EPS Lecture 2 Exp Class Lectures 1 / 23 Variables in Modeling the E ects of a
More informationECON 594: Lecture #6
ECON 594: Lecture #6 Thomas Lemieux Vancouver School of Economics, UBC May 2018 1 Limited dependent variables: introduction Up to now, we have been implicitly assuming that the dependent variable, y, was
More informationChapter 9 Regression with a Binary Dependent Variable. Multiple Choice. 1) The binary dependent variable model is an example of a
Chapter 9 Regression with a Binary Dependent Variable Multiple Choice ) The binary dependent variable model is an example of a a. regression model, which has as a regressor, among others, a binary variable.
More informationLecture 6: Discrete Choice: Qualitative Response
Lecture 6: Instructor: Department of Economics Stanford University 2011 Types of Discrete Choice Models Univariate Models Binary: Linear; Probit; Logit; Arctan, etc. Multinomial: Logit; Nested Logit; GEV;
More informationIntro Prefs & Voting Electoral comp. Political Economics. Ludwig-Maximilians University Munich. Summer term / 37
1 / 37 Political Economics Ludwig-Maximilians University Munich Summer term 2010 4 / 37 Table of contents 1 Introduction(MG) 2 Preferences and voting (MG) 3 Voter turnout (MG) 4 Electoral competition (SÜ)
More informationECON Introductory Econometrics. Lecture 11: Binary dependent variables
ECON4150 - Introductory Econometrics Lecture 11: Binary dependent variables Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 11 Lecture Outline 2 The linear probability model Nonlinear probability
More informationGeneralized Models: Part 1
Generalized Models: Part 1 Topics: Introduction to generalized models Introduction to maximum likelihood estimation Models for binary outcomes Models for proportion outcomes Models for categorical outcomes
More informationAn Overview of Choice Models
An Overview of Choice Models Dilan Görür Gatsby Computational Neuroscience Unit University College London May 08, 2009 Machine Learning II 1 / 31 Outline 1 Overview Terminology and Notation Economic vs
More information2. We care about proportion for categorical variable, but average for numerical one.
Probit Model 1. We apply Probit model to Bank data. The dependent variable is deny, a dummy variable equaling one if a mortgage application is denied, and equaling zero if accepted. The key regressor is
More informationCan a Pseudo Panel be a Substitute for a Genuine Panel?
Can a Pseudo Panel be a Substitute for a Genuine Panel? Min Hee Seo Washington University in St. Louis minheeseo@wustl.edu February 16th 1 / 20 Outline Motivation: gauging mechanism of changes Introduce
More informationProbabilistic Choice Models
Econ 3: James J. Heckman Probabilistic Choice Models This chapter examines different models commonly used to model probabilistic choice, such as eg the choice of one type of transportation from among many
More informationModeling Land Use Change Using an Eigenvector Spatial Filtering Model Specification for Discrete Response
Modeling Land Use Change Using an Eigenvector Spatial Filtering Model Specification for Discrete Response Parmanand Sinha The University of Tennessee, Knoxville 304 Burchfiel Geography Building 1000 Phillip
More informationStatistical Analysis of the Item Count Technique
Statistical Analysis of the Item Count Technique Kosuke Imai Department of Politics Princeton University Joint work with Graeme Blair May 4, 2011 Kosuke Imai (Princeton) Item Count Technique UCI (Statistics)
More informationGeneralized Linear Models for Non-Normal Data
Generalized Linear Models for Non-Normal 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 informationUNIVERSITY OF MARYLAND Department of Economics Economics 754 Topics in Political Economy Fall 2005 Allan Drazen. Exercise Set I
UNIVERSITY OF MARYLAND Department of Economics Economics 754 Topics in Political Economy Fall 005 Allan Drazen Exercise Set I The first four exercises are review of what we did in class on 8/31. The next
More informationOrdered Response and Multinomial Logit Estimation
Ordered Response and Multinomial Logit Estimation Quantitative Microeconomics R. Mora Department of Economics Universidad Carlos III de Madrid Outline Introduction 1 Introduction 2 3 Introduction The Ordered
More informationIntroduction to Generalized Models
Introduction to Generalized Models Today s topics: The big picture of generalized models Review of maximum likelihood estimation Models for binary outcomes Models for proportion outcomes Models for categorical
More informationDiscrete Choice Modeling
[Part 6] 1/55 0 Introduction 1 Summary 2 Binary Choice 3 Panel Data 4 Bivariate Probit 5 Ordered Choice 6 7 Multinomial Choice 8 Nested Logit 9 Heterogeneity 10 Latent Class 11 Mixed Logit 12 Stated Preference
More informationI. Multinomial Logit Suppose we only have individual specific covariates. Then we can model the response probability as
Econ 513, USC, Fall 2005 Lecture 15 Discrete Response Models: Multinomial, Conditional and Nested Logit Models Here we focus again on models for discrete choice with more than two outcomes We assume that
More informationcovariance between any two observations
1 Ordinary Least Squares (OLS) 1.1 Single Linear Regression Model assumptions of Classical Linear Regression Model (CLRM) (i) true relationship y i = α + βx i + ε i, i = 1,..., N where α, β = population
More informationSingle-level Models for Binary Responses
Single-level Models for Binary Responses Distribution of Binary Data y i response for individual i (i = 1,..., n), coded 0 or 1 Denote by r the number in the sample with y = 1 Mean and variance E(y) =
More informationThe Multilevel Logit Model for Binary Dependent Variables Marco R. Steenbergen
The Multilevel Logit Model for Binary Dependent Variables Marco R. Steenbergen January 23-24, 2012 Page 1 Part I The Single Level Logit Model: A Review Motivating Example Imagine we are interested in voting
More informationMaximum Likelihood and. Limited Dependent Variable Models
Maximum Likelihood and Limited Dependent Variable Models Michele Pellizzari IGIER-Bocconi, IZA and frdb May 24, 2010 These notes are largely based on the textbook by Jeffrey M. Wooldridge. 2002. Econometric
More informationECONOMETRICS HONOR S EXAM REVIEW SESSION
ECONOMETRICS HONOR S EXAM REVIEW SESSION Eunice Han ehan@fas.harvard.edu March 26 th, 2013 Harvard University Information 2 Exam: April 3 rd 3-6pm @ Emerson 105 Bring a calculator and extra pens. Notes
More informationLecture 12: Application of Maximum Likelihood Estimation:Truncation, Censoring, and Corner Solutions
Econ 513, USC, Department of Economics Lecture 12: Application of Maximum Likelihood Estimation:Truncation, Censoring, and Corner Solutions I Introduction Here we look at a set of complications with the
More information7/28/15. Review Homework. Overview. Lecture 6: Logistic Regression Analysis
Lecture 6: Logistic Regression Analysis Christopher S. Hollenbeak, PhD Jane R. Schubart, PhD The Outcomes Research Toolbox Review Homework 2 Overview Logistic regression model conceptually Logistic regression
More informationIntroduction to Linear Regression Analysis
Introduction to Linear Regression Analysis Samuel Nocito Lecture 1 March 2nd, 2018 Econometrics: What is it? Interaction of economic theory, observed data and statistical methods. The science of testing
More informationLatent Variable Models for Binary Data. Suppose that for a given vector of explanatory variables x, the latent
Latent Variable Models for Binary Data Suppose that for a given vector of explanatory variables x, the latent variable, U, has a continuous cumulative distribution function F (u; x) and that the binary
More informationStatistical Analysis of List Experiments
Statistical Analysis of List Experiments Graeme Blair Kosuke Imai Princeton University December 17, 2010 Blair and Imai (Princeton) List Experiments Political Methodology Seminar 1 / 32 Motivation Surveys
More informationLecture 1. Behavioral Models Multinomial Logit: Power and limitations. Cinzia Cirillo
Lecture 1 Behavioral Models Multinomial Logit: Power and limitations Cinzia Cirillo 1 Overview 1. Choice Probabilities 2. Power and Limitations of Logit 1. Taste variation 2. Substitution patterns 3. Repeated
More informationNew Approaches to Discrete Choice and Time-Series Cross-Section Methodology for Political Research
New Approaches to Discrete Choice and Time-Series Cross-Section Methodology for Political Research by Jonathan Kropko A dissertation submitted to the faculty of the University of North Carolina at Chapel
More informationModels for Heterogeneous Choices
APPENDIX B Models for Heterogeneous Choices Heteroskedastic Choice Models In the empirical chapters of the printed book we are interested in testing two different types of propositions about the beliefs
More informationCh 7: Dummy (binary, indicator) variables
Ch 7: Dummy (binary, indicator) variables :Examples Dummy variable are used to indicate the presence or absence of a characteristic. For example, define female i 1 if obs i is female 0 otherwise or male
More informationData Analytics for Social Science
Data Analytics for Social Science Johan A. Elkink School of Politics & International Relations University College Dublin 17 October 2017 Outline 1 2 3 4 5 6 Levels of measurement Discreet Continuous Nominal
More informationDiscrete Response Multilevel Models for Repeated Measures: An Application to Voting Intentions Data
Quality & Quantity 34: 323 330, 2000. 2000 Kluwer Academic Publishers. Printed in the Netherlands. 323 Note Discrete Response Multilevel Models for Repeated Measures: An Application to Voting Intentions
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 informationEPSY 905: Fundamentals of Multivariate Modeling Online Lecture #7
Introduction to Generalized Univariate Models: Models for Binary Outcomes EPSY 905: Fundamentals of Multivariate Modeling Online Lecture #7 EPSY 905: Intro to Generalized In This Lecture A short review
More informationFemale Wage Careers - A Bayesian Analysis Using Markov Chain Clustering
Statistiktage Graz, September 7 9, Female Wage Careers - A Bayesian Analysis Using Markov Chain Clustering Regina Tüchler, Wirtschaftskammer Österreich Christoph Pamminger, The Austrian Center for Labor
More informationStandard Errors & Confidence Intervals. N(0, I( β) 1 ), I( β) = [ 2 l(β, φ; y) β i β β= β j
Standard Errors & Confidence Intervals β β asy N(0, I( β) 1 ), where I( β) = [ 2 l(β, φ; y) ] β i β β= β j We can obtain asymptotic 100(1 α)% confidence intervals for β j using: β j ± Z 1 α/2 se( β j )
More informationBinary Logistic Regression
The coefficients of the multiple regression model are estimated using sample data with k independent variables Estimated (or predicted) value of Y Estimated intercept Estimated slope coefficients Ŷ = b
More informationLogit Regression and Quantities of Interest
Logit Regression and Quantities of Interest Stephen Pettigrew March 4, 2015 Stephen Pettigrew Logit Regression and Quantities of Interest March 4, 2015 1 / 57 Outline 1 Logistics 2 Generalized Linear Models
More informationIntroduction to Discrete Choice Models
Chapter 7 Introduction to Dcrete Choice Models 7.1 Introduction It has been mentioned that the conventional selection bias model requires estimation of two structural models, namely the selection model
More informationApplication of Latent Class with Random Effects Models to Longitudinal Data. Ken Beath Macquarie University
Application of Latent Class with Random Effects Models to Longitudinal Data Ken Beath Macquarie University Introduction Latent trajectory is a method of classifying subjects based on longitudinal data
More informationMULTINOMIAL LOGISTIC REGRESSION
MULTINOMIAL LOGISTIC REGRESSION Model graphically: Variable Y is a dependent variable, variables X, Z, W are called regressors. Multinomial logistic regression is a generalization of the binary logistic
More informationImmigration attitudes (opposes immigration or supports it) it may seriously misestimate the magnitude of the effects of IVs
Logistic Regression, Part I: Problems with the Linear Probability Model (LPM) Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 22, 2015 This handout steals
More informationModels of Qualitative Binary Response
Models of Qualitative Binary Response Probit and Logit Models October 6, 2015 Dependent Variable as a Binary Outcome Suppose we observe an economic choice that is a binary signal. The focus on the course
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 informationPolitical Economy of Institutions and Development. Lectures 2 and 3: Static Voting Models
14.773 Political Economy of Institutions and Development. Lectures 2 and 3: Static Voting Models Daron Acemoglu MIT February 7 and 12, 2013. Daron Acemoglu (MIT) Political Economy Lectures 2 and 3 February
More informationEconometric Modelling Prof. Rudra P. Pradhan Department of Management Indian Institute of Technology, Kharagpur
Econometric Modelling Prof. Rudra P. Pradhan Department of Management Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 28 LOGIT and PROBIT Model Good afternoon, this is doctor Pradhan
More informationProbabilistic Choice Models
Probabilistic Choice Models James J. Heckman University of Chicago Econ 312 This draft, March 29, 2006 This chapter examines dierent models commonly used to model probabilistic choice, such as eg the choice
More informationLecture 5: Spatial probit models. James P. LeSage University of Toledo Department of Economics Toledo, OH
Lecture 5: Spatial probit models James P. LeSage University of Toledo Department of Economics Toledo, OH 43606 jlesage@spatial-econometrics.com March 2004 1 A Bayesian spatial probit model with individual
More informationSTAT Chapter 13: Categorical Data. Recall we have studied binomial data, in which each trial falls into one of 2 categories (success/failure).
STAT 515 -- Chapter 13: Categorical Data Recall we have studied binomial data, in which each trial falls into one of 2 categories (success/failure). Many studies allow for more than 2 categories. Example
More informationWeek 7: Binary Outcomes (Scott Long Chapter 3 Part 2)
Week 7: (Scott Long Chapter 3 Part 2) Tsun-Feng Chiang* *School of Economics, Henan University, Kaifeng, China April 29, 2014 1 / 38 ML Estimation for Probit and Logit ML Estimation for Probit and Logit
More informationLogistic Regression: Regression with a Binary Dependent Variable
Logistic Regression: Regression with a Binary Dependent Variable LEARNING OBJECTIVES Upon completing this chapter, you should be able to do the following: State the circumstances under which logistic regression
More informationAnalysis of Categorical Data. Nick Jackson University of Southern California Department of Psychology 10/11/2013
Analysis of Categorical Data Nick Jackson University of Southern California Department of Psychology 10/11/2013 1 Overview Data Types Contingency Tables Logit Models Binomial Ordinal Nominal 2 Things not
More informationSOS3003 Applied data analysis for social science Lecture note Erling Berge Department of sociology and political science NTNU.
SOS3003 Applied data analysis for social science Lecture note 08-00 Erling Berge Department of sociology and political science NTNU Erling Berge 00 Literature Logistic regression II Hamilton Ch 7 p7-4
More informationEconometrics I Lecture 7: Dummy Variables
Econometrics I Lecture 7: Dummy Variables Mohammad Vesal Graduate School of Management and Economics Sharif University of Technology 44716 Fall 1397 1 / 27 Introduction Dummy variable: d i is a dummy variable
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 informationBinary Dependent Variables
Binary Dependent Variables In some cases the outcome of interest rather than one of the right hand side variables - is discrete rather than continuous Binary Dependent Variables In some cases the outcome
More informationTreatment Effects with Normal Disturbances in sampleselection Package
Treatment Effects with Normal Disturbances in sampleselection Package Ott Toomet University of Washington December 7, 017 1 The Problem Recent decades have seen a surge in interest for evidence-based policy-making.
More informationLecture-20: Discrete Choice Modeling-I
Lecture-20: Discrete Choice Modeling-I 1 In Today s Class Introduction to discrete choice models General formulation Binary choice models Specification Model estimation Application Case Study 2 Discrete
More informationLecture 14 More on structural estimation
Lecture 14 More on structural estimation Economics 8379 George Washington University Instructor: Prof. Ben Williams traditional MLE and GMM MLE requires a full specification of a model for the distribution
More informationSTA 303 H1S / 1002 HS Winter 2011 Test March 7, ab 1cde 2abcde 2fghij 3
STA 303 H1S / 1002 HS Winter 2011 Test March 7, 2011 LAST NAME: FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 303 STA 1002 INSTRUCTIONS: Time: 90 minutes Aids allowed: calculator. Some formulae
More informationEstimation of mixed generalized extreme value models
Estimation of mixed generalized extreme value models Michel Bierlaire michel.bierlaire@epfl.ch Operations Research Group ROSO Institute of Mathematics EPFL Katholieke Universiteit Leuven, November 2004
More informationApplied Economics. Regression with a Binary Dependent Variable. Department of Economics Universidad Carlos III de Madrid
Applied Economics Regression with a Binary Dependent Variable Department of Economics Universidad Carlos III de Madrid See Stock and Watson (chapter 11) 1 / 28 Binary Dependent Variables: What is Different?
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 informationMachine Learning. Lecture 3: Logistic Regression. Feng Li.
Machine Learning Lecture 3: Logistic Regression Feng Li fli@sdu.edu.cn https://funglee.github.io School of Computer Science and Technology Shandong University Fall 2016 Logistic Regression Classification
More informationDiscrete Choice Modeling
[Part 4] 1/43 Discrete Choice Modeling 0 Introduction 1 Summary 2 Binary Choice 3 Panel Data 4 Bivariate Probit 5 Ordered Choice 6 Count Data 7 Multinomial Choice 8 Nested Logit 9 Heterogeneity 10 Latent
More informationThe Generalized Roy Model and Treatment Effects
The Generalized Roy Model and Treatment Effects Christopher Taber University of Wisconsin November 10, 2016 Introduction From Imbens and Angrist we showed that if one runs IV, we get estimates of the Local
More informationReview of Multinomial Distribution If n trials are performed: in each trial there are J > 2 possible outcomes (categories) Multicategory Logit Models
Chapter 6 Multicategory Logit Models Response Y has J > 2 categories. Extensions of logistic regression for nominal and ordinal Y assume a multinomial distribution for Y. 6.1 Logit Models for Nominal Responses
More informationMS&E 226: Small Data
MS&E 226: Small Data Lecture 12: Logistic regression (v1) Ramesh Johari ramesh.johari@stanford.edu Fall 2015 1 / 30 Regression methods for binary outcomes 2 / 30 Binary outcomes For the duration of this
More informationChoice Theory. Matthieu de Lapparent
Choice Theory Matthieu de Lapparent matthieu.delapparent@epfl.ch Transport and Mobility Laboratory, School of Architecture, Civil and Environmental Engineering, Ecole Polytechnique Fédérale de Lausanne
More informationIntroduction to Econometrics
Introduction to Econometrics T H I R D E D I T I O N Global Edition James H. Stock Harvard University Mark W. Watson Princeton University Boston Columbus Indianapolis New York San Francisco Upper Saddle
More informationApplied Econometrics Lecture 1
Lecture 1 1 1 Università di Urbino Università di Urbino PhD Programme in Global Studies Spring 2018 Outline of this module Beyond OLS (very brief sketch) Regression and causality: sources of endogeneity
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 - ZERO-INFLATED POISSON REGRESSION SAS
More informationLecture 3.1 Basic Logistic LDA
y Lecture.1 Basic Logistic LDA 0.2.4.6.8 1 Outline Quick Refresher on Ordinary Logistic Regression and Stata Women s employment example Cross-Over Trial LDA Example -100-50 0 50 100 -- Longitudinal Data
More informationAn Activist Model of Democracy
5 An Activist Model of Democracy Norman Schofield Washington University 5.1. Introduction: A Stochastic Model of Elections The focus of this paper is that actual political systems do not appear to satisfy
More informationCOMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification
COMP 55 Applied Machine Learning Lecture 5: Generative models for linear classification Instructor: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/comp55 Unless otherwise noted, all material
More information