# Critical t-statistic This function calculates the critical t-statistic to limit the false discovery rate (Benjamini and Hochberg 1995) for a marginal effects plot to a specified level. ```r fdrInteraction(me.vec, me.sd.vec, df, type = "BH", level = 0.95) ``` ## Arguments - `me.vec`: A vector of marginal effects. - `me.sd.vec`: A vector of standard deviations for the marginal effects. - `df`: Degrees of freedom. - `type`: Should the BH (Benjamini and Hochberg 1999) or BY (Benjamini and Yekutieli 2000) correction be used? Options are "BH" (the default) or "BY". - `level`: The level of confidence. Defaults to 0.95. ## Returns The critical t-statistic for the interaction. ## Examples ```r ## Not run: data(legfig) # Clark and Golder 2006 replication data # limit to established democracies from the 1990s dat<-subset(legfig, subset=(nineties==1 & old==1)) lin.mod <- lm(enep1 ~ eneg + logmag + logmag_eneg + uppertier_eneg + uppertier + proximity1 + proximity1_enpres + enpres, data=dat) # save betas beta.mod <- coefficients(lin.mod) # save vcv vcv.mod <- vcov(lin.mod) # calculate MEs mag <- seq(from=0.01, to=5, by=0.01) me.vec <- beta.mod[2] + beta.mod[4]*mag me.se <- sqrt( vcv.mod[2,2] + (mag^2)*vcv.mod[4,4] + 2*(mag)*(vcv.mod[2,4]) ) ci.hi <- me.vec + 1.697 * me.se ci.lo <- me.vec - 1.697 * me.se plot(me.vec ~ mag, type="l", ylim = c(-4, 6)) lines(ci.hi ~ mag, lty=2) lines(ci.lo ~ mag, lty=2) fdrInteraction(me.vec, me.se, df=lin.mod$df, level=0.90) # 4.233986 ci.hi <- me.vec + 4.233986 * me.se ci.lo <- me.vec - 4.233986 * me.se lines(ci.hi ~ mag, lty=2, lwd=2) lines(ci.lo ~ mag, lty=2, lwd=2) abline(h=0, lty=1, col="gray") legend("topleft", lwd=c(1,2), lty=c(1,2), legend=c("90% CI", "90% FDR CI")) ## End(Not run) ``` ## References Benjamini, Yoav, and Yosef Hochberg. 1995. "Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing." **Journal of the Royal Statistical Society, Series B** 57(1): 289-300. Benjamini, Yoav, and Daniel Yekutieli. 2001. "The Control of the False Discovery Rate in Multiple Testing Under Dependency." **The Annals of Statistics** 29(4): 1165-1188. Clark, William R., and Matt Golder. 2006. "Rehabilitating Duverger's Theory." **Comparative Political Studies** 39(6): 679-708. Esarey, Justin, and Jane Lawrence Sumner. 2017. "Marginal Effects in Interaction Models: Determining and Controlling the False Positive Rate." **Comparative Political Studies** 51(9): 1144-1176. Esarey, Justin, and Jane Lawrence Sumner. 2018. "Corrigendum to 'Marginal Effects in Interaction Models: Determining and Controlling the False Positive Rate.'" ## Author(s) Justin Esarey and Jane Lawrence Sumner

fdrInteraction function