
1 
Paper

Mixed Logit Models in Political Science
Glasgow, Garrett

Uploaded 
07082001

Keywords 
mixed logit discrete choice heterogeneity

Abstract 
Mixed logit (MXL) is a general discrete choice model that is
applicable to a wide range of political science problems.
Mixed logit assumes the unobserved portions of utility are a
mixture of an IID extreme value term and another multivariate
distribution selected by the researcher. This general
specification allows MXL to avoid imposing the independence
of irrelevant alternatives (IIA) property on the choice
probabilities. Further, and more importantly, MXL is a
flexible tool for examining heterogeneity in individual
behavior through randomcoefficients specifications.
Three empirical examples are presented. Two are drawn
from studies of voting behavior. The first uses data
from the 1987 British general election and examines heterogeneity
in the impact of social class on voting, and the second uses
data from the 1992 U.S. presidential election and examines
heterogeneity in the impact of union membership on voting.
A third example examines heterogeneity in the factors that
lead to various Congressional career decisions. These empirical
examples demonstrate the utility of mixed logit in political
science research.
This paper has both a methodological and substantive contribution
for political science. Methodologically, it expands the tool set
available to researchers for studying various phenomena in
political science. More importantly, this paper contributes
substantively by allowing for more realistic models of individual
behavior. Most models currently used in political science
assume the independent variables have a homogeneous effect on the
dependent variable. This assumption is usually made to keep
models tractable, even though few believe it is an accurate
description of behavior. MXL is a tractable way to relax this
assumption and study heterogeneity in a variety of settings. 

2 
Paper

Correlated Disturbances in Discrete Choice Models:A Comparison of Multinomial Probit Models
Alvarez, R. Michael
Nagler, Jonathan

Uploaded 
01011995

Keywords 
econometrics logit multinomial probit gev discretechoice montecarlo

Abstract 
Correlated Disturbances in Discrete Choice Models:
A Comparison of Multinomial Probit Models and Logit Models
In political science, there are many cases where individuals make
discrete choices from more than two alternatives. This paper uses
Monte Carlo analysis to examine several questions about one class of
discrete choice models  those involving both alternativespecific
and individualspecific variables on the righthand side  and
demonstrates several findings.
First, the use of estimation techniques assuming uncorrelated disturbances
across alternatives in discrete choice models can lead to significantly
biased parameter estimates. This point is tempered by the observation that
probability estimates based on the full choice set generated from such
estimates are not likely to be biased enough to lead to incorrect inferences.
However, attempts to infer the impact of altering the choice set  such as
by removing one of the alternatives  will be less successful.
Second, the Generalized Extreme Value (GEV) model is extremely unreliable
when the pattern of correlation among the disturbances is not as restricted
as the GEV model assumes. GEV estimates may suggest grouping among the choices
that is in fact not present in the data.
Third, in samples the size of many typical political science applications
 1000 observations  Multinomial Probit (MNP) is capable of recovering
precise estimates of the parameters of the systemic component of the model,
though MNP is not likely to generate precise estimates of the relationship
among the disturbances in samples of this size.
Paradoxically, MNP's primary benefit is its ability to uncover relationships
among alternatives and to correctly estimate the affect of removing an
alternative from the choice set. Thus this paper suggests the increased
use of MNP by political scientists examining discrete choice problems when
the central question of interest is the effect of removing an alternative
from the choice set. We demonstrate that for other questions, models
positing independent disturbances may be `close enough.' 

3 
Paper

Issue Voting and Ecological Inference
Thomsen, Soren R.

Uploaded 
09142000

Keywords 
issue voting ecological inference electoral geography multinomial logit

Abstract 
This article proposes a unifying framework for individual and aggregate voting
behavior. The proposed individual level model is a version of the multinomial
logit model that applies to both issue voting, ideological voting and normative
voting providing a close fit to survey data. The aggregate model is derived by
using the binary logit model as an approximation to the multinomial logit model.
The aggregate model is useful for modeling electoral change and for identification
of homogenous political regions. Further, the unifying framework derives a method
for ecological inference that applies to large tables and gives estimates of voter transitions close to survery results. 

4 
Paper

When Politics and Models Collide: Estimating Models of MultiPartyElections
Alvarez, R. Michael
Nagler, Jonathan

Uploaded 
00000000

Keywords 
elections parties probit logit multinomial logit modelspecification spatial model multinomial probit discretechoice

Abstract 
Theory: The spatial model of elections can better be represented by
using conditional logit than by multinomial logit. The spatial model,
and random utility models in general, suffer from a failure to
adequately consider the substitutability of candidates sharing similar
or identical issue positions.
Hypotheses: Multinomial logit is not much better than successive
applications of binomial logit. Conditional logit allows for
considering more interesting political questions than does multinomial
logit. The spatial model may not correspond to voter decisionmaking
in multiplecandidate settings. Multinomial probit allows for a
relaxation of the IIA condition and this should improve estimates of
the effect of adding or removing parties.
Methods: Comparisons of binomial logit, multinomial logit, conditional
logit, and multinomial probit on simulated data and survey data from a
threeparty election.
Results: Multinomial logit offers almost no benefits
over binomial logit. Conditional logit is capable of examining
movements by parties, whereas multinomial logit is not. Multinomial
probit performs better than conditional logit when considering the
effects of altering the set of choices available to voters. 

5 
Paper

Is There a Gender Gap in Fiscal Political Preferences
Alvarez, R. Michael
McCaffery, Edward J.

Uploaded 
08122000

Keywords 
Gender gap fiscal politics taxation budget surplus multinomial logit missing data imputation framing survey experiments

Abstract 
This paper examines the relationship between
attitudes on potential uses of the budget surplus and
gender. Survey results show relatively weak support overall for using a
projected surplus to reduce taxes, with respondents much likelier to prefer
increased social spending on education or social security. There is a
significant gender gap with men being far more likely than women to support
tax cuts or paying down the national debt. Given a menu of particular types
of tax cuts, women are marginally more likely to favor childcare relief or
working poor tax credits whereas men are marginally more likely to favor
capital gains reduction or tax rate cuts. When primed that the tax laws are
biased against twoworker families, men significantly change their
preferences, moving from support for general tax rate cuts to support for
working poor tax relief, but not to childcare relief. One of the strongest
results to emerge is that women are far more likely than men not to express
an opinion or to confess ignorance about fiscal matters. Both genders
increase their ``no opinion'' answer in the face of priming, but men more so
than women. Further research will explore this no opinion/uncertainty aspect. 

6 
Paper

Information and American Attitudes Toward Bureaucracy
Alvarez, R. Michael
Brehm, John

Uploaded 
00000000

Keywords 
discrete choice logit probit heteroskedasticity ordered logit Internal Revenue Service ambivalence uncertainty

Abstract 
The exploration of American attitudes towards the Internal Revenue
Service joins an unusual pair of research domains: public opinion
and public administration. Public administration scholars contend
that the hostility Americans show towards ``bureaucracy'' stems from
the contradictory expectations Americans have for bureaucratic
performance. Drawing upon a survey commissioned by the IRS and
conducted in 1987 just after the passage of the Tax Reform Act, we
explore attitudes towards the performance of the IRS in eight
categories. Using a new heteroskedastic ordinal logit technique, we
demonstrate (1) that it is overwhelmingly a single expectation of
flexibility that governs attitudes towards the IRS; (2) that these
expectations are not in contradiction; and (3) that domainspecific
information sharply focuses respondent attitudes towards
bureaucracy. 

7 
Paper

Mixed Logit Models for Multiparty Elections
Glasgow, Garrett

Uploaded 
02242000

Keywords 
mixed logit random parameters logit multinomial probit IIA

Abstract 
This is a significantly updated version of my February 24 submission, with
several mathematical errors corrected and new information on multinomial
probit models and IIA violations.
In this paper I introduce the mixed logit (MXL), a flexible discrete
choice model based on random utility maximization. Mixed logit is the
most flexible discrete choice model available for the study of multiparty
and multicandidate elections  even more flexible than multinomial
probit (MNP), the discrete choice model currently favored for the study of
elections of this type.
Like MNP, MXL does not assume IIA, and can thus estimate realistic
substitution patterns between alternatives. In fact, MXL can be specified
to estimate the same substitution patterns as any specification of MNP.
Further, since the unobserved components of MXL are not constrained to
follow a normal distribution, and are not estimated as elements in a
covariance matrix, MXL can include any number of random coefficients or
error components that can follow any distribution. MXL is no more
difficult to estimate than MNP. An empirical example using data from the
1987 British general election demonstrates the utility of MXL in the study
of multicandidate and multiparty elections. 

8 
Paper

An Empirical Model of Government Formation in Parliamentary Democracies
Martin, Lanny W.
Stevenson, Randolph T.

Uploaded 
00000000

Keywords 
coalition theory government formation conditional logit econometrics

Abstract 
The study of coalition politics in parliamentary democracies
has led to the construction of several sophisticated theories
of government formation, but it has thus far failed to lead to the
development of a reliable method that will permit us to verify these
theories empirically. In this paper, we propose a solution to the
problems plaguing the application of multivariate statistical
analysis in this area. Specifically, we advocate use of the
conditional logit technique to model the government formation
process. We use this model to test various hypotheses from coalition
theory on an original data set consisting of information on every
potential government that could have formed in 285 separate instances
of coalition bargaining in 14 postwar parliamentary democracies.
We then illustrate further uses of this method by examining three
realworld cases of government formation. 

9 
Paper

Government Formation in Parliamentary Democracies
Martin, Lanny W.
Stevenson, Randolph T.

Uploaded 
01272000

Keywords 
government formation coalition politics conditional logit

Abstract 
The literature on cabinet formation in parliamentary democracies is
replete with theoretical explanations of why some cabinets form and others do
not. This theoretical richness, however, has not led to the development of a
healthy empirical literature designed to choose between competing theories. In
this paper, we try to rectify this problem by developing an empirical model that
can adequately capture the kind of choice situation that is inherent in cabinet
selection and then using it to evaluate the leading theories of cabinet
formation that have been advanced in the literature. For example, this analysis
allows us to make conclusions about the relative importance in cabinet formation
of traditional variables like size and ideology, as well as to evaluate the
impact that recent newinstitutionalist theories (such as Laver and Shepsle
1996) have on our ability to predict and explain cabinet formation over and
above the more traditional explanations. 

10 
Paper

Uncertainty and Ambivalence in the Ecology of Race
Alvarez, R. Michael
Brehm, John

Uploaded 
08221996

Keywords 
racial policy affirmative action ecological inference heteroskedastic ordered logit value conflict uncertainty ambivalence equivocation

Abstract 
Since Myrdal (1944), scholars have regarded American attitudes towards
racial policy as a conflict between values, groups, and interests.
Although Myrdal viewed the conflict as a state internal to individuals,
it begins as aggregate conflict. This mix of ecologiesindividual
and aggregatecarries forth to the present. This paper takes the
question of different ecologies for racial politics seriously,
developing tools to compare conflict at individual and aggregate level.
We demonstrate that individual racial policy choices stems principally
from racial resentment, and that the variability of that choice indicates
a state of uncertainty, not ambivalence or equivocation. We further
demonstrate that racial resentment does not surface as a predictor
of aggregate racial policy choice, even though individual choices
about racial policies appear to be more
strongly influenced by the level of political informedness. 

11 
Paper

Testing for Interaction in Models with Binary Dependent Variables
Berry, William D.

Uploaded 
04081999

Keywords 
probit logit scobit interaction binary dependent variables

Abstract 
Over the last decade, political scientists have proposed several
strategies for testing hypotheses about interaction in models
with binary dependent variables. I argue that these strategies
are incomplete, and propose an alternative approach. Consistent
with Nagler's (1991; 1994) and Frant's (1991) advice, this approach
involves including multiplicative terms in probit, logit and scobit
models to specify interaction. However, the information used to
test the hypotheses about interaction depends on whether the
dependent variable of conceptual interest is the observed
dichotomous variable or a latent, unbounded, continuous variable
which the observed dichotomy is assumed to measure. In the latter
case, hypotheses about interaction are tested by examining
directly the maximum likelihood estimates of the coefficients
for the multiplicative terms. In the former situation,
the propositions are tested by analyzing changes in the
predicted probability that the observed dependent variable will
equal one of its values associated with changing values of the
independent variables. 

12 
Paper

Beyond Ordinary Logit: Taking Time Seriously in Binary TimeSeriesCrossSection Models
Beck, Nathaniel
Katz, Jonathan
Tucker, Richard

Uploaded 
08221997

Keywords 
binary timeseriescrosssection data logit/probit temporal dependence grouped duration models complementary loglog cubic spline economic interdependence democratic peace war

Abstract 
Researchers typically analyze timeseriescrosssection data with a
binary dependent variable (BTSCS) using ordinary logit or probit.
However, BTSCS observations are likely to violate the independence
assumption of the ordinary logit or probit statistical model. It is
well known that if the observations are temporally related that the
results of an ordinary logit or probit analysis may be misleading. In
this paper, we provide a simple diagnostic for temporal dependence and
a simple remedy. Our remedy is based on the idea that
BTSCS data is identical to grouped duration data. This remedy does
not require the BTSCS analyst to acquire any further methodological
skills and it can be easily implemented in any standard
statistical software package. While our approach is suitable for any
type of BTSCS data, we provide examples and applications from the
field of International Relations, where BTSCS data is frequently used.
We use our methodology to reassess Oneal and Russett's (1997) findings
regarding the relationship between economic interdependence,
democracy, and peace. Our analyses show that 1) their finding that
economic interdependence is associated with peace is an artifact of
their failure to account for temporal dependence and 2)
their finding that democracy inhibits conflict is upheld even taking
duration dependence into account. 

13 
Paper

Heterogeneity in the Impact of Issues on Vote Choice
Glasgow, Garrett

Uploaded 
04181999

Keywords 
random parameters logit heterogeneity issue salience

Abstract 
There is a great deal of diversity in the issues than members of the
American electorate are concerned with.
It seems logical that these different concerns will lead voters to
evaluate political candidates in different ways when voting.
Unfortunately, the models currently employed by political scientists
ignore the possibility of heterogeneity in the weights that individuals
place on issues when voting. In order to create a tractable model of
vote choice, most researchers assume that the weights placed on issues
are homogeneous across voters. Estimating such a model tells us if
an issue was salient to the electorate on average, but gives us no
information about heterogeneity in the use of the issue.
Allowing for heterogeneity in issue weights allows for a much more complete
picture of the impact of issues on vote choice. I assume that issue
weights are distributed among voters by
some known probability distribution, and estimate the parameters of that
distribution. This assumption leads to random parameters logit. I
present the results of a random parameters logit model for the 1996
presidential election, and compare these results to those from a conditional
logit model with the homogeneity assumption. I show that random parameters
logit contains all of the information that models that assume homogeneity do,
plus I uncover evidence of heterogeneity in the weights placed on issues
by voters. 

14 
Paper

Conflict, Information, and Lobbying Coalitions
Esterling, Kevin M.

Uploaded 
08181997

Keywords 
Policy Alliances Organizational Deliberation Nested Logit

Abstract 
This paper explains lobbying organizations' choice to join alliances
on policy matters with respect to 1) the degree of the organization's
access to external information sources, and 2) the amount of internal
organizational conflict and deliberation. An informational view of
lobbying suggests that the more informed an organizational actor is,
the more likely it will gain access to governmental decision makers;
and greater access to the government will decrease the utility of
joining a cooperative lobbying effort. In addition, internal conflict in
the definition of a policy position will limit an organization's ability
to take any position on a policy issue, while successful internal
deliberation will augment a lobbying organization's ability to find
cooperation partners. Outcome and explanatory data are taken from
an existing dataset housed at ICPSR. Nested logit maximum
likelihood estimates for the trichotomouschoice cooperation model
are presented and interpreted. Support is lent to both the internal
conflict and the informational theories of cooperation in policy
lobbying. In particular, the model results suggest that organizations
predisposed to internal conflict find both nonpolicy lobbying and
cooperative lobbying appealing, suggesting that these organizations
only sometimes successfully deliberate over policy. And consistent
with the information view of lobbying, greater access to information
sharply decreases the utility of lobbying cooperatively. 

16 
Paper

Heterogeneity, Salience, and Voter Decision Rules for Candidate Preference
Glasgow, Garrett

Uploaded 
08101997

Keywords 
voter behavior decision rules rank ordered logit salience issue voting

Abstract 
Voters in American Presidential elections display a wide variety of decision
rules when choosing a candidate. One form of this heterogeneity is
differential weighting of issues used to make a vote choice. The structure
of this heterogeneity and differential salience of issues has important
implications for the American political process. Determining
the nature of these heterogeneous preferences is vital to understanding
electoral politics in the United States. An empirical technique for
modeling and exploring heterogeneity is developed and applied to the
1980 NES Panel Study. I show that heterogeneity in voter decision
rules is widespread, and that while many voters rely on nonissue
considerations when determining candidate preference, issue voting does
play a role in the decision rules of many voters. 

17 
Paper

Logistic Regression in Rare Events Data
King, Gary
Zeng, Langche

Uploaded 
05201999

Keywords 
rare events logit logistic regression binary dependent variables bias correction casecontrol choicebased endogenous selection selection bias

Abstract 
Rare events are binary dependent variables with dozens to thousands
of times fewer ones (events, such as wars, vetoes, cases of
political activism, or epidemiological infections) than zeros
(``nonevents''). In many literatures, rare events have proven
difficult to explain and predict, a problem that seems to have at
least two sources. First, popular statistical procedures, such as
logistic regression, can sharply underestimate the probability of
rare events. We recommend corrections that outperform existing
methods and change the estimates of absolute and relative risks by
as much as some estimated effects reported in the literature.
Second, commonly used data collection strategies are grossly
inefficient for rare events data. The fear of collecting data with
too few events has led to data collections with huge numbers of
observations but relatively few, and poorly measured, explanatory
variables, such as in international conflict data with more than a
quarter million dyads, only a few of which are at war. As it turns
out, easy procedures exist for making valid inferences when sampling
all available events (e.g., wars) and a tiny fraction of nonevents
(peace). This enables scholars to save as much as 99% of their
(nonfixed) data collection costs, or to collect much more
meaningful explanatory variables. We provide methods that link
these two results, enabling both types of corrections to work
simultaneously, and software that implements the methods developed. 

18 
Paper

Estimation and Strategic Interaction in Discrete Choice Models of International Conflict
Signorino, Curtis S.

Uploaded 
07231997

Keywords 
discrete choice strategic QRE logit international relations

Abstract 
Typical applications of logit and probit to theories of
international conflict do not capture the structure of the
strategic interdependence implied by those theories. In this
paper I demonstrate how to use a gametheoretic solution concept,
the quantal response equilibrium (QRE), to derive strategic
discrete choice models of international conflict, where the
structure of the strategic interaction is incorporated directly
in the statistical model. I demonstrate this for a crisis
interaction model and use monte carlo analysis to show that logit
provides estimates with incorrect substantive interpretations and
fitted values that are often far from the true values. Finally,
I reanalyze a wellknown gametheoretic model of war, Bueno de
Mesquita and Lalman's (1992) international interaction game, using
this method. My results indicate that their model does not
explain international interaction as well as they claim. 

19 
Paper

Inference from ResponseBased Samples with Limited Auxiliary Information
King, Gary
Zeng, Langche

Uploaded 
07091999

Keywords 
rare events logit logistic regression binary dependent variables bias correction casecontrol choicebased endogenous selection selection bias epidemiology

Abstract 
This paper is for the methods conference;
it is related to "Logistic Regression in
Rare Events Data," also by us; the conference
presentation will be based on both papers.
We address a disagreement between epidemiologists and
econometricians about inference in responsebased (a.k.a.
casecontrol, choicebased, retrospective, etc.) samples.
Epidemiologists typically make the rare event assumption (that the
probability of disease is arbitrarily small), which makes the
relative risk easy to estimate via the odds ratio. Econometricians
do not like this assumption since it is false and implies that
attributable risk (a.k.a. a first difference) is zero, and they
have developed methods that require no auxiliary information. These
methods produce bounds on the quantities of interest that,
unfortunately, are often fairly wide and always encompass a
conclusion of no treatment effect (relative risks of 1 or
attributable risks of 0) no matter how strong the true effect is.
We simplify the existing bounds for attributable risk, making it
much easier to estimate, and then suggest one possible resolution of
the disagreement by providing a method that allows researchers to
include easily available information (such as that the fraction of
the population with the disease falls within at most [.001,.05]);
this method considerably narrows the bounds on the quantities of
interest. We also offer software to implement the methods
suggested.
We would very much appreciate any comments you might have! 

22 
Paper

A Panel Probit Analysis of Campaign Contributions and Roll Call Votes
Wawro, Gregory

Uploaded 
09071999

Keywords 
campaign finance panel data methods logit probit random effects GMM estimators

Abstract 
Political scientists have long been concerned with the effects of campaign
contributions on roll call voting. However, methodological problems have
hampered attempts to assess the degree to which contributions affect voting.
One of the key problems is that it is difficult to untangle the effect of
contributions from the effect of a member's predisposition to vote one way or
another. That is, political action committees (PACs) contribute to members of
Congress who are likely to vote the way the PACs favor even in the absence of
contributions. A PAC donation to a friendly member might be misconstrued as
causing a member to vote a particular way, when in reality the member would
have voted that way to begin with. It is therefore crucial to account for a
member's propensity to vote in a particular way in order to assess the
influence of contributions. One way that studies have done this is to use
ideological ratings developed by interest groups. This approach is
problematic, however, because the ratings are built from roll call votes and
thus will introduce bias if campaign contributions affect the votes used to
compute the ratings. In order to circumvent the problem of accounting for
voting predispositions, I use panel data methods which, unfortunately, have
seen almost no application in political science. These methods enable us to
account for individual specific effects which are difficult or impossible to
measure, such as the predisposition to vote for or against a particular type
of legislation. To employ these methods, I build panels of roll call votes on
legislation that business and labor groups have indicated are important for
their interests. Using panel data estimators, I determine the effects of
contributions from corporate and labor PACs on the probability of voting
``aye'' or ``nay'', while accounting for members' propensities to vote in
particular directions. I find that contributions have minimal to no effects
on roll call votes, while shortterm factors including monthly unemployment
and support for the president in the district have substantial effects. 

24 
Paper

Have Turnout Effects Really Declined? Testing the Partisan Implications of Marginal Voters
Gill, Jeff
Martinez, Michael

Uploaded 
08092002

Keywords 
voting turnout partisan effects simulation multinomial logit

Abstract 
In this paper, we review the theoretical foundations of the debate about whether
higher election turnout advantages left parties, suggest a method of assessing
the effects of turnout within a single election, and provide evidence from four
U.S. elections that the partisan effects of turnout are contingent on the
strength and polarity of the shortterm forces. Our methodological approach to
addressing whether the Democrats would have benefited from higher turnout (and
whether the Republicans would have benefited from lower turnout) in a given
election is to employ a new type of simulation based on multinomial logit
estimates of the choices made by individual citizens.
Our substantive approach is similar to Lacy and Burden (1999), in that we posit
that U.S. citizens have three unordered choices in each election: vote
Democratic, vote Republican, or abstain. We first estimate vote choice (including
the abstention category) as an unordered multinomial logit function of standard
variables associated with both candidate preference and the likelihood of voting.
From that estimation, we derive probabilities for each respondent's selection of
each of the three choices (abstain, vote Democratic, or vote Republican). From
those probabilities, we simulate several levels of turnout. Higher turnout is
simulated by progressively adding to the pool of voters actual abstainers with
the lowest probability of abstaining of those remaining in the pool of abstainers.
Whereas lower turnout is simulated by progressively subtracting from the
electorate actual voters with the highest probability of abstaining.
Our results across the four elections provide partial support for both the
conventional SESbased model and the alternative defectionbased model, though
neither model's predictions are completely borne out empirically. As predicted by
the conventional model, we find that the electorate has a greater Democratic tilt
at higher levels of turnout, although that relationship has significantly weakened
over time. 

25 
Paper

Public Opinion Shocks and Government Termination
Martin, Lanny W.

Uploaded 
11161999

Keywords 
government survival public opinion discretehazard model logit

Abstract 
Abstract. The ability of a government to remain in power depends partially upon
its vulnerability to unexpected changes occurring in the outside political
environment. In this paper, I examine the relationship between government
termination and changes in the electoral expectations of political parties in
the legislature, as reflected by shifts in popular support for the government.
I find that the decision to terminate the government is related in complex ways
to changes in public opinion. Governments are more likely to collapse as
certain members of the incumbent coalition expect to gain more ministerial
portfolios, and in cases of minority government, when the opposition expects to
gain more legislative seats. Further, I show that these effects increase with
the approach of regularlyscheduled elections. 

26 
Paper

Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?
Berry, William
Esarey, Justin
DeMeritt, Jacqueline

Uploaded 
05062007

Keywords 
interaction logit probit

Abstract 
Political scientists presenting binary dependent variable (BDV) models often offer hypotheses that independent variables interact in their influence on the probability that an event Y occurs, Pr(Y). A consensus appears to have evolved on how to test such hypotheses: (i) estimate a logit or probit model including product terms to specify the interaction, (ii) test the hypothesis by determining whether the coefficients for these terms are statistically significant, and (iii) if they are, describe the nature of the interaction by estimating how the marginal effect of one independent variable on Pr(Y) varies with the value of the other independent variables. We contend that in the BDV context, statistically significant product term coefficients are neither necessary nor sufficient for concluding that there is substantively meaningful interaction among variables in their influence on Pr(Y). Even when no product terms are included in a logit or probit model, if the marginal effect of one variable on Pr(Y) is related to another independent variable then substantively meaningful interaction is present, and describing such interaction is essential to an accurate portrayal of the data generating process at work. We propose a strategy for studying interaction in the BDV context that is consistent with the recent emphasis in the discipline on casting hypotheses in terms of effects on the probability of an event's occurrence and reporting estimated marginal effects on this probability. 

27 
Paper

StateLevel Opinions from National Surveys: Poststratification using Hierarchical Logistic Regression
Park, David K.
Gelman, Andrew
Bafumi, Joseph

Uploaded 
07122002

Keywords 
Bayesian Inference Hierarchical Logit Poststratification Public Opinion States Elections

Abstract 
Previous researchers have pooled national surveys in order to construct
statelevel opinions. However, in order to overcome the small n problem
for less populous states, they have aggregated a decade or more of
national surveys to construct their measures. For example, Erikson,
Wright and McIver (1993) pooled 122 national surveys conducted over 13
years to produce statelevel partisan and ideology estimates. Brace,
SimsButler, Arceneaux, and Johnson (2002) pooled 22 surveys over a
25year period to produce statelevel opinions on a number of specific
issues. We construct a hierarchical logistic regression model for the
mean of a binary response variable conditional on poststratification
cells. This approach combines the modeling approach often used in
smallarea estimation with the population information used in
poststratification (see Gelman and Little 1997). We produce statelevel
estimates pooling seven national surveys conducted over a nineday
period. We first apply the method to a set of U.S preelection polls,
poststratified by state, region, as well as the usual demographic
variables and evaluate the model by comparing it to statelevel election
outcomes. We then produce statelevel partisan and ideology estimates by
comparing it to Erikson, Wright and McIver's estimates. 

28 
Paper

Operationalizing and Testing Spatial Theories of Voting
Quinn, Kevin M.
Martin, Andrew D.

Uploaded 
04151998

Keywords 
spatial voting factor analysis multinomial probit multinomial logit Bayesian inference model comparison Bayes factors MCMC Dutch politics Danish politics

Abstract 
Spatial models of voting behavior provide the foundation for a
substantial number of theoretical results. Nonetheless, empirical
work involving the spatial model faces a number of potential
difficulties. First, measures of the latent voter and candidate issue
positions must be obtained. Second, evaluating the fit of competing
statistical models of voter choice is often more complicated than
previously realized. In this paper, we discuss precisely these
issues. We argue that confirmatory factor analysis applied to
masslevel issue preference questions is an attractive means of
measuring voter ideal points. We also show how party issue positions
can be recovered using a variation of this strategy. We go on to
discuss the problems of assessing the fit of competing statistical
models (multinomial logit vs. multinomial probit) and competing
explanations (those based on spatial theory vs. those derived from
other theories of voting such as sociological theories). We
demonstrate how the Bayesian perspective not only provides
computational advantages in the case of fitting the multinomial probit
model, but also how it facilitates both types of comparison mentioned
above. Results from the Netherlands and Denmark suggest that even
when the computational cost of multinomial probit is disregarded, the
decision whether to use multinomial probit (MNP) or multinomial logit
(MNL) is not clearcut. 

29 
Paper

Estimating Binary Dependent Variable Models Under Conditions of Specification Uncertainty
Berry, William
DeMeritt, Jacqueline
Esarey, Justin

Uploaded 
01252007

Keywords 
logit probit binary dependent variable specification uncertainty interaction Monte Carlo analysis

Abstract 
Political scientists routinely use logit or probit models when their data involve binary dependent variables (BDVs). Yet the hypotheses we test with logit and probit are rarely specific enough to justify that one of these models is the correct functional form for the process (or true model) generating the data. In this situation of specification uncertainty, it is reasonable to assume that the model being estimated is misspecified. The only issue is the severity of the resulting distortion in results, i.e., whether logit or probit approximates the true model well enough to yield estimated effects that are acceptably close to the true ones. To study estimation in the presence of specification uncertainty, we conduct Monte Carlo analysis using a strategy of purposeful misspecification: we use various logit and probit models with different terms on data sets generated from a wide range of known true models involving a BDV, none of which takes the exact form of a logit or probit model. We find that a widelyemployed approach for using logit or probit to test the hypothesis that an independent variable has a positive (or negative) effect on the probability that some event will occurby estimating the effect of the variable at central values of the independent variablesis highly forgiving of specification uncertainty, yielding reasonably accurate inferences even when the true model is not logit or probit. Unfortunately, other applications of logit and probitincluding a common approach to testing a hypothesis that independent variables interact in influencing the probability of event occurrenceare not nearly as forgiving of the uncertainty. In some situations of specification uncertainty, we can improve the quality of estimated effects by relying on the Akaike Information Criterion [AIC] to choose the terms to be included in a model, but even these improved estimates leave much to be desired. 

30 
Paper

Turnout Effects on the Composition of the Electorate: A Multinomial Logit Simulation of the 2000 Presidential Election
Martinez, Michael

Uploaded 
03182002

Keywords 
turnout multinomial logit simulation

Abstract 
Conventional wisdom among pundits and some scholars posits that higher turnout should
benefit liberal parties, since lower socioeconomic classes comprise a disproportionate
share of the nonvoting population. Empirical tests of this prediction across elections
have produced a wide variety of results, ranging from support for the conventional
wisdom to suggestions that Republicans benefit from higher turnout to null findings.
In this paper, we provide a simulation of the possible impact of increasing or
decreasing turnout in a single election. Using data from the 2000 American National
Election Study, we find that Gore would have benefitted slightly from higher turnout
and would have been harmed slightly by lower turnout, but the overall magnitude of the
effects of turnout on Gore's share of the two party vote is small. At higher levels of
turnout, Democrats comprise a larger share of the electorate, but they also have a
higher defection rate. 

31 
Paper

The Problem with Quantitative Studies of International Conflict
Beck, Nathaniel
King, Gary
Zeng, Langche

Uploaded 
07151998

Keywords 
Conflict logit neural networks forecasting Bayesian analysis

Abstract 
Despite immense data collections, prestigious journals, and
sophisticated analyses, empirical findings in the literature on
international conflict are frequently unsatisfying. Statistical
results appear to change from article to article and specification
to specification. Very few relationships hold up to replication
with even minor respecification. Accurate forecasts are
nonexistent. We provide a simple conjecture about what accounts for
this problem, and offer a statistical framework that better matches
the substantive issues and types of data in this field. Our model,
a version of a ``neural network'' model, forecasts substantially
better than any previous effort, and appears to uncover some
structural features of international conflict. 

32 
Paper

New Empirical Strategies to Model the Government
Formation Process
Glasgow, Garrett
Golder, Matt
Golder, Sona

Uploaded 
07152010

Keywords 
discrete choice mixed logit IIA random coefficients government formation

Abstract 
Over the past decade, a "standard approach" to the quantitative study of government formation has developed. This approach involves the use of a conditional (CL) logit model to examine government choice with the government formation opportunity as the unit of analysis. In this paper, we reconsider this approach and
make three methodological contributions. First, we demonstrate that the existing procedure used to test for the independence of irrelevant alternatives (IIA) is ﬂawed and severely biased against ﬁnding IIA violations.
Our new testing procedure reveals that many government alternatives share unobserved attributes, thereby violating the IIA assumption and making the CL model inappropriate. Second, we employ a mixed logit with random coefficients that allows us to take account of unobserved heterogeneity and IIA violations. Third, we return to a question that originally motivated this literature, namely, what determines the likelihood that
a particular party enters government? Although scholars have generally abandoned this question due to perceived methodological limitations in our ability to address it, we demonstrate that calculating probabilities
for parties entering ofﬁce rather than governments is straightforward in a mixed logit framework. 

33 
Paper

Heterogeneity in Discrete Choice Models
Glasgow, Garrett

Uploaded 
12122001

Keywords 
heterogeneity discrete choice logit probit ambivalence

Abstract 
Nearly all empirical studies of individual behavior in political science have sought to
estimate the mean relationship between some variables of interest. While such studies are
vital for determining aggregate relationships between variables of interest, they are an
incomplete picture of individual behavior. In particular, we generally do not pay attention
to the possibility of heterogeneity, or individuallevel variation in the relationships
we estimate. Ignoring heterogeneity in our models means we are ignoring valuable information
about individual behavior. This paper demonstrates that examining heterogeneity in
discrete choice models is both important substantively and feasible methodologically.
Possible sources of heterogeneity are discussed, and it is shown that these sources
of heterogeneity are observationally equivalent in most cases, meaning it is generally
not possible to determine the source of heterogeneity in our empirical models.
Several empirical models for examining heterogeneity are described. An empirical example
studying heterogeneity in union voting in the 1992 US presidential election demonstrates the 

34 
Paper

Modeling Direction and Intensity in Ordinal Scales with Midpoints
Jones, Bradford S.
Sobel, Michael E.

Uploaded 
07211998

Keywords 
adjacent category logit loglinear models public opinion Congress

Abstract 
Political opinion analysts are frequently work with
semantically balanced ordinal scales. Such
survey items are frequently used to measure candidate
evaluations, public spending preferences,
positions on social issues, and candidate
and party placement. Because of the special nature of
these survey items (semantically balanced about a
midpoint), researchers may be interested in understanding
how both the response direction and response intensity
varies over time and/or across covariate classes. That
is, trends may be found in the tendency for respondents
to choose categories above vs. below the midpoint
(the response direction) and trends may be found in
the tendency for respondents to choose between or among
category labels above or below the midpoint. And
while political analysts are commonly interested in
response intensity and direction, traditional
methods used to model distributions on semantically
balanced ordinal scales are problematic. In this
paper, we discuss a class of models originally
developed by Sobel (1995, 1997, 1998) that allows
researchers to simultaneously model direction and
intensity in ordinal scales with midpoints.
Specifically, we parameterize the model as an
adjacent category logit model. Numerous
parsimonious models may be arrived at that describe
trends in the response direction and response intensity.
Because the adjacent category logit model is linear in the logits,
we estimate the model using loglinear models. We
present an application of the models to data
on approval ratings of House incumbents. We find that
the trends in response directions (the
tendency for respondents to evaluate the
incumbent favorably or not favorably) increase through
the 1980s, peaking in the late Eighties, and are
now declining over the 1990s. With regard to
response intensity, (that is, the tendency to
respond in the extreme categories vs. the moderate
categories), we find that intensity increases during
most presidential election cycles and vanishes
during midterm election years. We argue this finding
is related to the different levels of political
information citizens are exposed to in presidential
vs. midterm election cycles. 

35 
Paper

Modeling History Dependence in NetworkBehavior Coevolution
Franzese, Robert
Hays, Jude
Kachi, Aya

Uploaded 
07212010

Keywords 
path dependence history dependence network coevolution spatial econometrics selection homophily SIENA RSIENA markov chain logit pstar military alliance conflict behavior

Abstract 
Spatial interdependencethe dependence of outcomes in some units on those in othersis
substantively and theoretically ubiquitous and central across the social sciences. Spatial association is also omnipresent empirically. However, spatial association may arise from three importantly distinct processes: common exposure of actors to exogenous external and internal stimuli, interdependence of outcomes/behaviors across actors (contagion), and/or the putative outcomes may affect the variable along which the clustering occurs (selection). Accurate inference about any of these processes generally requires an empirical strategy that addresses
all three well. From a spatialeconometric perspective, this suggests spatiotemporal empirical models with exogenous covariates (common exposure) and spatial lags (contagion), with the spatial weights being endogenous (selection). From a longitudinal networkanalytic perspective, we can identify the same three processes as potential sources of network effects and network formation. From that perspective, actors' selfselection into networks (by, e.g., behavioral homophily) and actors' behavior that is contagious through those network connections likewise demands theoretical and empirical models in which networks and behavior coevolve over time.
This paper begins building such modeling by, on the theoretical side, extending a Markov typeinteraction model to allow endogenous tieformation, and, on the empirical side, merging a simple spatiallag logit model of contagious behavior with a simple pstar logit model of network formation, building this synthetic discretetime empirical model from the theoretical base of the modified Markov typeinteraction model. One interesting consequence of networkbehavior coevolutionidentically: endogenous patterns of spatial interdependenceemphasized here is how it can produce historydependent political dynamics, including equilibrium phat and path dependence (Page 2006). The paper explores these implications, and then concludes with a preliminary demonstration of the strategy applied to alliance formation and conflict behavior among the great powers in the first half of the twentieth century. 

36 
Paper

An Agenda for New Political Methodology: Microfoundations and ART
Achen, Christopher H.

Uploaded 
08292001

Keywords 
logit probit scobit microfoundations

Abstract 
The last two decades have brought revolutionary change to the field of
political methodology. Steady gains in theoretical sophistication have
combined with explosive increases in computing power to produce a profusion
of new estimators for applied political researchers. Attendance at the annual
Summer Meeting of the Methodology Section has multiplied many times, and
section membership is among the largest in APSA. All these are signs of
success. Yet there are warning signs, too. This paper, written to appear in
the {em Annual Review of Political Science}, attempts to critically
summarize current developments in the young field of political methodology.
It focuses on recent generalizations of dichotomous dependent variable
estimators like logit and probit, arguing that even our best new work stands
in need of firmer connection to credible models of human behavior and more
sophisticated work habits for discovering reliable empirical generalizations. 

37 
Paper

The Spatial Model and Specification of Choice Models
Alvarez, R. Michael
Nagler, Jonathan

Uploaded 
01011995

Keywords 
Multinomial Logit Spatial Model Conditional Logit Elections

Abstract 
The spatial model has been in use in political science for close
to 30 years, and in that period it has achieved a place of prime importance as
our paradigm of the process of candidatechoice used by voters.
For much of this time political scientists have estimated models of
candidatechoice using binary logit or probit, even in cases where
there were more than two choices facing voters. Recently
discrete choices models beyond binary logit and probit have been making
their way into use in political science with increasing frequency.
The properties of these models, and their relationship to the spatial
model, are frequently misunderstood. This paper
demonstrates four essential points. First, the popular multinomial logit
model is in fact equivalent to running a series of binary logit
models. It involves nothing more than pairwise comparisons of the
choices. Second, despite containing no information about the
choices, the multinomial logit model provides reduced form
estimates of the effect
of characteristics of choices that are equivalent to the estimates
of such effects provided by the conditional logit model  which does
utilize information about the characteristics of the choices. Third, the
multinomial logit model cannot offer any inferences as to effects of changing
the characteristics of the choices, or introducing additional choices;
whereas the conditional logit model can offer such inferences. Fourth, the
classic spatial model has a flaw in multicandidate settings that has been
overlooked, with more than two candidates the spatial model explicitly
contradicts an aspect
of voter behaviour widely believed to be prevalent: the tendency of
voters to view certain candidates as `similar' alternatives, and thus
for the presence of additional candidates to effect asymettrically
the probability of existing candidates being chosen. 

