×

Kernel-based semiparametric multinomial logit modelling of political party preferences. (English) Zbl 1332.62427

Summary: Conventional, parametric multinomial logit models are in general not sufficient for capturing the complex structures of electorates. In this paper, we use a semiparametric multinomial logit model to give an analysis of party preferences along individuals’ characteristics using a sample of the German electorate in 2006. Germany is a particularly strong case for more flexible nonparametric approaches in this context, since due to the reunification and the preceding different political histories the composition of the electorate is very complex and nuanced. Our analysis reveals strong interactions of the covariates age and income, and highly nonlinear shapes of the factor impacts for each party’s likelihood to be supported. Notably, we develop and provide a smoothed likelihood estimator for semiparametric multinomial logit models, which can be applied also in other application fields, such as, e.g., marketing.

MSC:

62P25 Applications of statistics to social sciences
91F10 History, political science
62G08 Nonparametric regression and quantile regression
62-07 Data analysis (statistics) (MSC2010)

Software:

rgl

References:

[1] Abe M (1998) Measuring consumers nonlinear brand choice response to price. J Retail 74:541-568 · doi:10.1016/S0022-4359(99)80107-9
[2] Abe M (1999) A generalized additive model for discrete-choice data. J Bus Econ Stat 17:271-284
[3] Adler D, Murdoch D (2009) Package ‘rgl’—3D visualization device system (OpenGL). http://rgl.neoscientists.org
[4] Akima H (1978) A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans Math Softw 4:148-164 · Zbl 0387.65010 · doi:10.1145/355780.355786
[5] Ben-Akiva M, Lerman SL (1985) Discrete choice analysis: theory and application to travel demand. The MIT Press, Cambridge, MA
[6] Curtice J, Firth D (2008) Exit polling in a cold climate: the BBCITV experience in Britain in 2005. J R Stat Soc Series A 171:509-539 · doi:10.1111/j.1467-985X.2007.00536.x
[7] Domencich T, McFadden D (1975) Urban travel demand: a behavioral analysis. North-Holland publishing Co., Amsterdam · Zbl 1072.62034
[8] Dow JK, Endersby JW (2004) Multinomial probit and multinomial logit: a comparison of choice models for voting research. Elect Stud 23:107-122 · doi:10.1016/S0261-3794(03)00040-4
[9] Fisher SD, Ford R, Jennings W, Pickup M, Wlezien C (2011) From polls to votes to seats: forecasting the, 2010 British general election. Elect Stud 30:250-257 · doi:10.1016/j.electstud.2010.09.005
[10] Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102:359-378 · Zbl 1284.62093 · doi:10.1198/016214506000001437
[11] Härdle W, Huet S, Mammen E, Sperlich S (2004a) Bootstrap inference in semiparametric generalized additive models. Econ Theory 20:265-300 · Zbl 1072.62034 · doi:10.1017/S026646660420202X
[12] Härdle W, Müller M, Sperlich S, Werwatz A (2004b) Nonparametric and semiparametric models. Springer Series in Statistics, Berlin · Zbl 1059.62032 · doi:10.1007/978-3-642-17146-8
[13] Hastie TJ, Tibshirani RJ (1986) Generalized additive models. Stat Sci 1:297-318 · Zbl 0955.62603 · doi:10.1214/ss/1177013604
[14] Hausman J, McFadden D (1984) Specification tests for the multinomial logit model. Econometrica 52:1219-1240 · Zbl 0564.62095 · doi:10.2307/1910997
[15] Kalyanaram D, Little JDC (1994) An empirical analysis of latitude of price acceptance in consumer package goods. J Consumer Res 21:408-418 · doi:10.1086/209407
[16] Kneib T, Baumgartner B, Steiner WJ (2007) Semiparametric multinomial logit models for analysing consumer choice behaviour. Adv Stat Anal 91:225-244 · Zbl 1331.62477 · doi:10.1007/s10182-007-0033-2
[17] Köhler M, Schindler A, Sperlich S (2014) A review and comparison of bandwidth selection methods for Kernel regression. Int Stat Rev (in press) · Zbl 1416.62216
[18] Krishnamurthi L, Raj SP (1988) A model of brand choice and purchase quantity price sensitivities. Market Sci 7:1-20 · doi:10.1287/mksc.7.1.1
[19] Lösche P (1993) Kleine Geschichte der deutschen Parteien. Kohlhammer, Stuttgart · Zbl 1109.62310
[20] McFadden D (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P (ed) Frontiers in econometrics, Academic Press, New York, pp 105-142 · Zbl 0387.65010
[21] Müller M (2001) Estimation and testing in gerneralized partial linear models: a comparative study. Stat Comput 11:299-309 · doi:10.1023/A:1011981314532
[22] Quinn KM, Martin AD, Whitford AB (1999) Voter choice in multi-party democracies: a test of competing theories and models. Am J Political Sci 43:1231-1247 · doi:10.2307/2991825
[23] Roca-Pardinas J, Sperlich S (2010) Feasible estimation in generalized structured models. Stat Comput 20:367-379 · doi:10.1007/s11222-009-9130-2
[24] Severini TA, Wong WH (1992) Generalized profile likelihood and conditionally parametric models. Ann Stat 20:1768-1802 · Zbl 0768.62015 · doi:10.1214/aos/1176348889
[25] Small KA, Hsiao C (1985) Multinomial logit specification tests. Int Econ Rev 26:619-627 · Zbl 0592.62099 · doi:10.2307/2526707
[26] Sperlich S, Tjøstheim D, Yang L (2002) Nonparametric estimation and testing of interaction in additive models. Econ Theory 18:197-251 · Zbl 1109.62310 · doi:10.1017/S0266466602182016
[27] Tutz G, Scholz T (2004) Semiparametric modelling of multicategorical data. J Stat Comput Simul 74:183-200 · Zbl 1048.62047 · doi:10.1080/0094965031000118959
[28] Walter F (2008) Baustelle Deutschland. Suhrkamp, Frankfurt am Main · Zbl 0592.62099
[29] Yee TW, Wild CJ (1996) Vector generalized additive models. J R Stat Soc B 58:481-493 · Zbl 0855.62059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.