Making predictions

Bayesian Regression Modeling with rstanarm

Jake Thompson

Psychometrician, ATLAS, University of Kansas

Making predictions for observed data

stan_model <- stan_glm(kid_score ~ mom_iq + mom_hs, data = kidiq)

posteriors <- posterior_predict(stan_model)
posteriors[1:10, 1:5]

              1         2         3         4         5
 [1,]  61.08989  58.57298  80.68946 101.00810  76.37946
 [2,] 111.52704  49.92284  99.09657  97.33291  72.98906
 [3,]  83.36793  81.35768  94.16414 101.73570  64.69375
 [4,] 118.15092  74.00476 107.28852  75.75912  91.93991
 [5,] 103.95042  58.98491 128.40312 121.42753  62.70008
 [6,] 102.29874 127.74050  84.10661  67.94056  82.02546
 [7,]  91.39445  88.49029  75.05702  94.48594 102.50331
 [8,]  93.33446  84.99589 101.49261  66.74698  68.26968
 [9,] 101.85065  91.46998 123.43011  76.53226  74.93288
[10,]  79.61489 101.29745 105.97636  97.48332  99.80582

Making predictions for new data

predict_data <- data.frame(
  mom_iq = 110,
  mom_hs = c(0, 1))

predict_data

  mom_iq mom_hs
1    110      0
2    110      1

Making predictions for new data

new_predictions <- posterior_predict(stan_model, 
                         newdata = predict_data)

new_predictions[1:10,]

              1         2
 [1,]  90.90581 107.75710
 [2,]  78.72466 139.86677
 [3,]  80.67743  88.81523
 [4,]  83.47852  74.06063
 [5,]  69.07708  87.81177
 [6,]  40.46229  85.45969
 [7,]  79.41597  64.19011
 [8,] 107.93867 117.49345
 [9,]  95.31493  82.51476
[10,]  91.18056  94.22732

summary(new_predictions[, 1])

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
20.90   75.26   87.64   87.68  100.02  156.00

summary(new_predictions[, 2])

 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
34.78   81.32   93.49   93.66  105.62  159.82

Let's practice

Bayesian Regression Modeling with rstanarm