Specifying a Model of State Policy Innovation

Frant, Howard; Berry, Frances Stokes; Berry, William D.

doi:10.2307/1963176

Cited by 23 publications

(27 citation statements)

References 4 publications

(8 reference statements)

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“…This interaction is assumed by the model specification. (Nagler 1991(Nagler , 1397 A similar exchange occurred between Berry and Berry (1990) and Frant (1991). Berry and Berry published conclusions that independent variables interact in influencing the probability of a lottery adoption by an American state based on results from a probit model including no product terms.…”

Section: The Prevailing View About Testing For Interaction In Logit Amentioning

confidence: 99%

“…Nagler (1994, 250) argues that meaningful interaction must be "variable specific" and therefore modeled with product terms involving the interacting variables. Any finding of interaction from a model without a product term-or from a model with a product term that proves statistically insignificant-is an "artifact of the methodology," and thus substantively meaningless (Nagler 1991(Nagler , 1393; see also Brambor, Clark, and Golder 2006, 77;Frant 1991).…”

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confidence: 99%

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Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?

Berry¹,

DeMeritt

Esarey

2009

American J Political Sci

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354

301

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Political scientists presenting binary dependent variable (BDV) models often hypothesize that variables interact to influence the probability of an event, Pr (Y ). The current typical approach to testing such hypotheses is (1) estimate a logit or probit model with a product term, (2) test the hypothesis by determining whether the coefficient for this term is statistically significant, and (3) characterize the nature of any interaction detected by describing how the estimated effect of one variable on Pr(Y ) varies with the value of another. This approach makes a statistically significant product term necessary to support the interaction hypothesis. We show that a statistically significant product term is neither necessary nor sufficient for variables to interact meaningfully in influencing Pr(Y ). Indeed, even when a logit or probit model contains no product term, the effect of one variable on Pr(Y ) may be strongly related to the value of another. We present a strategy for testing for interaction in a BDV model, including guidance on when to include a product term. M any phenomena important to political scientists are binary outcomes: an event occurs (Y = 1), or it does not (Y = 0). 1 Political scientists studying binary dependent variables (BDVs) frequently hypothesize that two independent variables interact in influencing the probability that the event will occur, 2 i.e., that the effect of one independent variable William D. journals published 77 quantitative articles analyzing binary dependent variables, representing 41% of all the empirical articles in these journals.2 Indeed, of the 77 articles presenting BDV models in the journals referenced in note 1, 26-over one-third-test hypotheses that one or more variables interact. 3 To be more precise, X 1 is said to interact with X 2 in influencing the probability that the event will occur [i.e., Prob(Y = 1)] if given an increment in X 1 [from X 1(lo) to X 1(hi) ] and an increment in X 2 [from X 2(lo) to X 2(hi) ],When both increments are infinitesimal, this requires that the second derivative, ∂ 2 Prob(Y = 1)/∂X 1 ∂X 2 , be different from zero. When the difference in X 1 is infinitesimal, but the difference in X 2 is discrete, this requires that the marginal effect of X 1 on Prob(Y = 1) [i.e., the first derivative, ∂Prob(Y = 1)/∂X 1 ] has different values at X 2(lo) and X 2(hi) . When both increments are discrete, this requires that a second difference in probabilities be nonzero.(X 1 ) on this probability is conditional on the value of the other (X 2 ). 3 Typically, current practice is to test this hypothesis using logit or probit, being guided by two recommendations from the political methodology literature.First, scholars have wisely been urged to focus on the presentation and interpretation of substantively relevant quantities-in the BDV context, the probability

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Section: The Prevailing View About Testing For Interaction In Logit Amentioning

confidence: 99%

mentioning

confidence: 99%

Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?

Berry¹,

DeMeritt

Esarey

2009

American J Political Sci

Self Cite

354

301

View full text Add to dashboard Cite

show abstract

“…As might be anticipated, the bulk of the results from the base 17 However, note that interpreting marginal effects of interaction variables in nonlinear models remains highly controversial. While marginal effects provide a sense of practical importance, calculating the cross derivative of the expected value of the dependent variable in nonlinear models has been criticized as potentially resulting in artificial and atheoretical predictions (Frant, 1991). The functional form of a nonlinear model implies that all explanatory variables have nonlinear effects on the probability of interest.…”

Section: Multivariate Estimatesmentioning

confidence: 99%

Profit sharing and firm size: The role of team production

Heywood¹,

Jirjahn²

2009

Journal of Economic Behavior & Organization

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“…However, while it is relatively straightforward to estimate and interpret interaction effects in linear models, this is not the case in logit models, and there is no consensus in the field about the most appropriate way to do this (Berry & Berry, 1991;Berry, 1999;Nagler, 1994;Norton et al, 2004). There are several difficulties with interpreting the marginal effects and signs of interaction term coefficients in the same way as one would do in linear models, and the familiar odds-ratio interpretation cannot be applied (Ai & Norton, 2003;Norton et al, 2004).…”

Section: Modelling Voting Behaviour In Referendumsmentioning

confidence: 99%