mcmcObsProb | R Documentation |

Implements R function to calculate the predicted probabilities for "observed" cases after a Bayesian logit or probit model, following Hanmer & Kalkan (2013) (2013, American Journal of Political Science 57(1): 263-277).

mcmcObsProb( modelmatrix, mcmcout, xcol, xrange, xinterest, link = "logit", ci = c(0.025, 0.975), fullsims = FALSE )

`modelmatrix` |
model matrix, including intercept (if the intercept is among the
parameters estimated in the model). Create with model.matrix(formula, data).
Note: the order of columns in the model matrix must correspond to the order of columns
in the matrix of posterior draws in the |

`mcmcout` |
posterior distributions of all logit coefficients,
in matrix form. This can be created from rstan, MCMCpack, R2jags, etc. and transformed
into a matrix using the function as.mcmc() from the coda package for |

`xcol` |
column number of the posterior draws ( |

`xrange` |
name of the vector with the range of relevant values of the explanatory variable for which to calculate associated Pr(y = 1). |

`xinterest` |
semi-optional argument. Name of the explanatory variable for which
to calculate associated Pr(y = 1). If |

`link` |
type of generalized linear model; a character vector set to |

`ci` |
the bounds of the credible interval. Default is |

`fullsims` |
logical indicator of whether full object (based on all MCMC draws
rather than their average) will be returned. Default is |

This function calculates predicted probabilities for "observed" cases after a Bayesian logit or probit model following Hanmer and Kalkan (2013, American Journal of Political Science 57(1): 263-277)

if `fullsims = FALSE`

(default), a tibble with 4 columns:

x: value of variable of interest, drawn from

`xrange`

median_pp: median predicted Pr(y = 1) when variable of interest is set to x

lower_pp: lower bound of credible interval of predicted probability at given x

upper_pp: upper bound of credible interval of predicted probability at given x

if `fullsims = TRUE`

, a tibble with 3 columns:

Iteration: number of the posterior draw

x: value of variable of interest, drawn from

`xrange`

pp: average predicted Pr(y = 1) of all observed cases when variable of interest is set to x

Hanmer, Michael J., & Ozan Kalkan, K. (2013). Behind the curve: Clarifying the best approach to calculating predicted probabilities and marginal effects from limited dependent variable models. American Journal of Political Science, 57(1), 263-277. https://doi.org/10.1111/j.1540-5907.2012.00602.x

if (interactive()) { ## simulating data set.seed(12345) b0 <- 0.2 # true value for the intercept b1 <- 0.5 # true value for first beta b2 <- 0.7 # true value for second beta n <- 500 # sample size X1 <- runif(n, -1, 1) X2 <- runif(n, -1, 1) Z <- b0 + b1 * X1 + b2 * X2 pr <- 1 / (1 + exp(-Z)) # inv logit function Y <- rbinom(n, 1, pr) df <- data.frame(cbind(X1, X2, Y)) ## formatting the data for jags datjags <- as.list(df) datjags$N <- length(datjags$Y) ## creating jags model model <- function() { for(i in 1:N){ Y[i] ~ dbern(p[i]) ## Bernoulli distribution of y_i logit(p[i]) <- mu[i] ## Logit link function mu[i] <- b[1] + b[2] * X1[i] + b[3] * X2[i] } for(j in 1:3){ b[j] ~ dnorm(0, 0.001) ## Use a coefficient vector for simplicity } } params <- c("b") inits1 <- list("b" = rep(0, 3)) inits2 <- list("b" = rep(0, 3)) inits <- list(inits1, inits2) ## fitting the model with R2jags library(R2jags) set.seed(123) fit <- jags(data = datjags, inits = inits, parameters.to.save = params, n.chains = 2, n.iter = 2000, n.burnin = 1000, model.file = model) ### observed value approach library(coda) xmat <- model.matrix(Y ~ X1 + X2, data = df) mcmc <- as.mcmc(fit) mcmc_mat <- as.matrix(mcmc)[, 1:ncol(xmat)] X1_sim <- seq(from = min(datjags$X1), to = max(datjags$X1), length.out = 10) obs_prob <- mcmcObsProb(modelmatrix = xmat, mcmcout = mcmc_mat, xrange = X1_sim, xcol = 2) }

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