Bayesian logit model with Pólya Gamma prior with MCMC
Usage
mnlogit(X, Y, baseline = ncol(Y), niter = 1000, nburn = 500, A0 = 10^4)Arguments
- X
An n by k matrix of explanatory variables
- Y
An n by p matrix of dependent variables
- baseline
Baseline class for estimation. Parameters will be set to zero. Defaults to the p-th column.
- niter
Total number of MCMC draws
- nburn
Burn-in draws for MCMC
- A0
Prior variance scalar for all slope coefficients
Value
A list containing
postbA k x p x (niter - nburn dimensions) array containing posterior draws of the slope coefficients.marginal_fxA k x p x (niter - nburn dimensions) array containing posterior draws of marginal effects.X, Y, baselineThe matrices of explanatory and dependent variables, as defined above and the baseline class.
References
Nicholas G. Polson, James G. Scott, and Jesse Windle. Bayesian inference for logistic models using Polya-Gamma latent variables. Journal of the American statistical Association 108.504 (2013): 1339-1349.
Examples
n <- 100
p <- 3
k <- 2
X <- cbind(1, matrix(rnorm(n * (k - 1), 0, 2), n, k - 1))
BETA <- matrix(sample(c(-3:3), k * p, replace = TRUE), k, p)
BETA[, p] <- 0
Y <- exp(X %*% BETA) / rowSums(exp(X %*% BETA))
res1 <- mnlogit(X, Y)
#>
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print(BETA)
#> [,1] [,2] [,3]
#> [1,] -3 1 0
#> [2,] 3 -3 0
print(apply(res1$postb, c(1, 2), mean))
#> [,1] [,2] [,3]
#> [1,] -3.309630 1.235649 0
#> [2,] 3.245753 -3.852727 0
require(tidyr)
Y = dplyr::filter(argentina_luc,lu.from == "Cropland" & Ts == 2000) %>%
pivot_wider(names_from = lu.to)
X = argentina_df$xmat %>% tidyr::pivot_wider(names_from = "ks") %>%
dplyr::arrange(match(ns,Y$ns))
Y = Y %>% dplyr::select(-c(lu.from,Ts,ns))
X = X %>% dplyr::select(-c(ns))
res1 <- mnlogit(as.matrix(X), as.matrix(Y),baseline = which(colnames(Y) == "Cropland"),
niter = 100,nburn = 50)
#>
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print(apply(res1$postb, c(1, 2), mean))
#> Cropland Forest OtherLand Pasture
#> Intercept 0 -3.796285e+00 -5.8772331073 -7.656935e+00
#> Cropland 0 -6.183014e-03 0.0031790380 -2.351784e-02
#> Forest 0 -2.170406e-02 0.0052990212 5.178866e-03
#> OtherLand 0 8.710393e-03 -0.0125493881 -9.181244e-03
#> Pasture 0 2.100400e-03 0.0004128899 4.825130e-03
#> Plantations 0 -2.582314e-02 -0.2219133925 -3.710696e-02
#> Urban 0 -1.014442e-03 -0.8361251782 -4.874117e+00
#> MeanTemp 0 -7.260722e-03 0.0273925055 -2.245136e-03
#> MeanPrecip 0 -5.410051e-04 -0.0004399593 -2.266767e-04
#> HarvWood 0 1.142146e-02 0.5454130018 3.392572e-02
#> HarvCost 0 3.737684e-04 -0.0032157449 5.899610e-04
#> GRASYLD 0 -1.903381e-01 -0.0214090318 5.002190e-02
#> meanTimeToMarket 0 -3.871487e-03 -0.0006335591 9.403948e-04
#> totPop 0 -2.707342e-04 -0.0001508931 -1.520544e-04
#> ruralPop 0 2.623296e-01 -0.7562659797 -9.096202e-01
#> Altitude 0 -1.026486e-03 0.0005487423 -2.940524e-04
#> Slope 0 2.796321e-02 0.0254912940 -3.140357e-02
#> Soil2_Medium 0 -1.134372e+00 -0.6925383063 2.659172e+00
#> Soil3_Heavy 0 4.065724e-01 -0.9644933834 3.973145e+00
#> Soil4_Stony 0 -1.009990e+00 -0.2342204054 -2.249419e+00
#> MEANYLD 0 -5.795987e+01 7.7719622311 -3.258236e+01
#> HI_MEAN 0 1.666235e+01 -4.2353022799 1.781134e+01
#> LI_MEAN 0 1.225341e+01 0.5377789658 -4.120644e+00
#> IR_MEAN 0 1.394622e+01 -2.1287763538 7.549424e+00
#> SS_MEAN 0 1.540385e+01 -1.6446134950 1.141858e+01
#> Plantations Urban
#> Intercept -1.408002e+01 -1.528958e+01
#> Cropland -1.136966e-02 1.246410e-02
#> Forest 4.585718e-03 -9.783224e-03
#> OtherLand 3.803265e-03 5.789315e-03
#> Pasture -5.408957e-03 -2.935421e-03
#> Plantations -9.436381e-03 -4.095200e-01
#> Urban -5.209868e-01 -6.680181e-01
#> MeanTemp 7.575193e-03 7.062805e-04
#> MeanPrecip -1.017311e-04 -1.656599e-04
#> HarvWood 5.762479e-01 1.747155e+00
#> HarvCost -2.430452e-03 -2.265119e-02
#> GRASYLD 1.626919e-02 -1.181236e-01
#> meanTimeToMarket 1.362148e-03 5.523938e-04
#> totPop 1.181234e-05 -1.398674e-04
#> ruralPop -1.517320e+00 7.038877e-01
#> Altitude -3.016830e-04 -7.122637e-04
#> Slope -3.609381e-02 -1.489167e-01
#> Soil2_Medium 9.190299e+00 9.486333e+00
#> Soil3_Heavy 1.092553e+01 1.091791e+01
#> Soil4_Stony 8.473508e+00 9.945717e+00
#> MEANYLD 7.976525e+00 -2.504058e+01
#> HI_MEAN 1.460317e+00 -7.083513e+00
#> LI_MEAN -3.323083e+00 2.206426e+01
#> IR_MEAN -3.411697e+00 6.138944e+00
#> SS_MEAN -2.656811e+00 4.157459e+00