Estimating Legislators Ideal Points Using HOMALS

Transcription

1 Estimating Legislators Ideal Points Using HOMALS Applied to party-switching in the Brazilian Chamber of Deputies, 49th Session, Scott W. Desposato, UCLA,

2 Party-Switching: Substantive Questions Some Facts: 1/3 of Brazilian Deputies Switch party during their 4year term Some change as many as 8 times Switching is slightly less common among leftist parties Some Questions: Do deputies limit the ideological distances of their switching? Do deputies change their voting behavior after switching? Both questions require spatial representations of legislators

3 The HOMALS Method for Spatial Representation: Given: n = number of observations, J = number of variables, p = number of solution dimensions X is an nxp matrix of object scores; Gj is an indicator matrix for the jth variable, and Yj is a matrix of category quantifications for the jth variable; HOMALS Minimizes: Estimation in three steps via Alternating Least Squares : (1) Y G X (category quantifications are the average of their object scores) j = 1 j X = ( G Y ) (2) (object scores are the average of their category quantifications) J j j i= 1 (3) Normalize to : X X = ni (scale, avoids collapse to a single point) See: de Leeuw (1996), Gifi (1990). 1 J J j= 1 SSQ( X GjYj) u X = 0 (center on origin)

4 Graphical Intuition for HOMALS: Randomly plot the legislators and the votes points in p space Draw lines from the legislators to each of their positions (yes or no votes) Move the legislators and the vote positions until the sum of all lines lengths is minimized (See below)

5 An example: HOMALS finds locations that minimize the line lengths Vote 1 Party ID Vote 2 Vote 3 Blue dot = PFL (center-right) Red dot = PMDB (center-left) Magenta dot = PT (Leftist workers party)

6 Brazilian Legislators Voting Behavior in Two Dimensions 6 PSTU PST PSDB PSD 4 PSC PSB PRONA 2 PRN PPR PP 0 PMN PMDB PL -2 PFL PDT PDS -4 PDC PCdB PCDOB PCB

7 Range of Party Centroids Spanned by Party-Switching 3 Party Range Spanned by Switching, First Dimension Left Center Right

8 Do Deputies vote differently after changing party? Distribution of Relative Proximity to New and Old Parties Closer to old party Didn t change voting behavior.89 Mean.56 SE of Mean Closer to new party

9 Nominate vs HOMALS (Using U.S. Senate Data) DNOM1 DNOM2 Pearson Correlation DNOM1 DNOM2 Homals D1 Homals D2 Correlations Homals Homals DNOM1 DNOM2 D1 D ** ** ** ** **. Correlation is significant at the 0.01 level (2-tailed). Homals D1 Homals D2 PID Republican Democrat

10 HOMALS in Comparative Perspective Advantages Not just binary - can include multiple categories Easy, intuitive, and relatively fast to program and run Missing and fuzzy data easy to incorporate Bootstrapping gives standard errors Highly correlated with Nominate Similar to Poole s (1997) Nonparametric Method

11 HOMALS Disadvantages Where s the model? This technique comes out of the Gifi school of multivariate analysis, rather than a model-driven approach. Parameter Proliferation Problem: Practically, we ll never have real power over our estimates: adding legislators or adding votes will increase the number of parameters to estimate. Instability: Like NOMINATE, estimates are unstable and adjustments required when dealing with extreme voters or when missing excessive data. Solution: Passive observations.

12 References Efron, B. and Tibshirani, R Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Sciences. 1:1. p Gifi, Albert Nonlinear Multivariate Analysis. Chichester: Wiley. Hoffman, Donna L. and de Leeuw, Jan Interpreting Multiple Correspondence Analysis as an MDS Method. Unpublished manuscript. Londregan, John L Estimating Preferences from Voting Records. Forthcoming. Michailidis, George and de Leeuw, Jan The Gifi System of Nonlinear Multivariate Analysis. Unpublished manuscript Poole, Keith T Non-Parametric Analysis of Binary Choice Data. Working paper. Poole, Keith T, and Rosenthal, Howard Patterns of Congressional Voting. American Journal of Political Science. 35:1. p Special thanks to John Londregan, Mohan Penubarti, and Jan de Leeuw

13 Other Programs and Projects Samples at: Object-oriented programming in Xlisp-Stat: An animated program to re-map the Southwest using flight times and multi-dimensional scaling (mds) A program to simulate Congressional elections (written for John Zaller, UCLA) A program for case-deletion diagnostics in GLS A program for importance sampling Other: An SPSS job to compare HOMALS and Nominate