NPC: Nonparametric Combination of Dependent Hypothesis Tests

In NPC: Nonparametric Combination of Hypothesis Tests

Description

This function conducts multiple hypothesis tests under the sharp null of no effects and combines the results into a single global p-value.

Usage

NPC(data, keep = TRUE, tr.var, tr.label, y.vars, comb.fun = "ProductCF",
    n.perms = 1000, block.var = NULL, clust.var = NULL, event.var = NULL,
    alternative = "greater", seed = 1, na.rm = TRUE, FWE.adj = TRUE,
    step.down = identical(comb.fun, "MinimumCF"),
    test.statistic = "StudentsT", return.matrix = FALSE, print.steps = TRUE,
    adapt.test = logical(length(y.vars)))

Arguments

data	Data frame with treatment, response, and other variables
keep	Subset of observations (default keeps all)
tr.var	Name of treatment variable (character)
tr.label	Level of 'tr.var' indicating treated units (character)
y.vars	Names of response variables (character)
comb.fun	Combining function (character or function)
n.perms	Number of permutations, in addition to the one observed
block.var	Variable defining blocks within which to restrict permutations (character)
clust.var	Variable defining clusters of observations assigned to treatment en bloc (character)
event.var	Logical variable indicating whether duration variables were observed rather than censored (character)
alternative	Scalar or vector indicating the alternative hypotheses ("greater", "less", or "two.sided"). If "less", test statistics are multiplied by -1. If "two.sided", the absolute value is used.
seed	Random seed (numeric)
na.rm	Delete observations with missing values? (logical)
FWE.adj	Calculate FWE-adjusted p-values? (logical)
step.down	If performing FWE adjustment, use stepdown MinP? (logical)
test.statistic	Vector or list of test statistic functions (possibly quoted) for marginal tests. If single value is given, then it is used for all marginal tests.
return.matrix	Return the permutation distribution of test statistics and p-values? (logical)
print.steps	Print progress of the function? (logical)
adapt.test	Use the adaptive test of Hogg et al. (1975)? (logical vector)

Value

p.values	vector of marginal p-values plus the joint NPC p-value
p.matrix	(optional) matrix containing the permutation distribution of marginal p-values
T.matrix	(optional) matrix containing the permutation distribution of test statistics

Author(s)

Devin Caughey <[e-mail]>

References

Caughey, Devin, Allan Dafoe, and Jason Seawright. Forthcoming. “Nonparametric Combination (NPC): A Framework for Testing Elaborate Theories.” Journal of Politics.

Chung, EunYi, and Joseph P. Romano. 2013. “Exact and Asymptotically Robust Permutation Tests.” Annals of Statistics 41 (2): 484-507.

Hogg, Robert V., Doris M. Fisher, and Ronald H. Randles. 1975. “A Two-Sample Adaptive Distribution-Free Test.” Journal of the American Statistical Association 70 (351): 656-661.

Pesarin, Fortunato, and Luigi Salmaso. 2010. Permutation Tests for Complex Data. Chichester, UK: Wiley.

Examples

library(NPC)
## Required for this example
library(mvtnorm)
library(car)

## COVARIANCE = CORRELATION = 0.25
cov <- 0.25
N <- 8
Tr <- c(rep(0, 4), rep(1, 4))
d1 <- 1
d2 <- 1
d3 <- 1
sd <- 1
sigma <-
    matrix(c(1, cov, cov, cov, 1, cov, cov, cov, 1), ncol = 3)
## Create error matrix
set.seed(2)
ee <- rmvnorm(N, c(0, 0, 0), sigma)
mean(c(cor(ee)[1, 2], cor(ee)[3, 2], cor(ee)[1, 3]))

Y1 <- -.5 + Tr*d1 + ee[, 1]
Y2 <- -.5 + Tr*d2 + ee[, 2]
Y3 <- -.5 + Tr*d3 + ee[, 3]
## Create data
(ex.dta <- data.frame(Tr, Y1, Y2, Y3))
(diffs <- round(colMeans(subset(ex.dta, Tr == 1, -Tr)) -
                colMeans(subset(ex.dta, Tr == 0, -Tr)), 2))
mean(diffs)
## NPC
npc.out <- NPC(data=ex.dta, tr.var="Tr", tr.label=1,
               y.vars=c("Y1", "Y2", "Y3"), n.perms=1000,
               alternative = "greater", seed=1, comb.fun="NormalCF",
               test.statistic="DiffMeans", FWE.adj=FALSE)
round(npc.out$p.value, 2) ## one-sided
##>   Y1   Y2   Y3  NPC
##> 0.25 0.05 0.07 0.08

## Compare with T-tests and MANOVA
t.test(Y1 ~ Tr, var.equal = TRUE, alternative = "less")
t.test(Y2 ~ Tr, var.equal = TRUE, alternative = "less")
t.test(Y3 ~ Tr, var.equal = TRUE, alternative = "less")
car::Anova(lm(cbind(Y1, Y2, Y3) ~ Tr)) ## two-sided

NPC documentation built on May 2, 2019, 5:07 a.m.