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分类数据分析

贝叶斯分类模型

贝叶斯篇
R 
library(tidyverse)
library(tidybayes)
library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())

数据

这里，我们模拟了500个人他的家庭收入和职业选择 (career = 1, 2, 3)

R 
df <- readr::read_rds(here::here("demo_data", "career.rds")) 
df

以 career = 3为基线(baseline)，我们要估计下面公式中的四个参数，

💡

回想下logit回归的数学表达式

$$ \begin{align*} log\left(\frac{P(\text{career}=1)}{P(\text{career}=3)}\right) &= \alpha_{1} + \beta_{1} \text{income} \\

log\left(\frac{P(\text{career}=2)}{P(\text{career}=3)}\right) &= \alpha_{2} + \beta_{2} \text{income} \\ \end{align*} $$

多项Logistic回归模型，R语言可以使用 nnet::multinom() 函数

R 
df %>% 
  dplyr::mutate(career = fct_rev(as_factor(career))) %>% 
  nnet::multinom(career ~ family_income, data = .)

stan for multi-logit Regression

stan 1

R 
stan_program <- &quot;
data{
    int N;              // number of observations
    int K;              // number of outcome values
    int career[N];      // outcome
    real family_income[N];
}
parameters{
    vector[K-1] a;      // intercepts
    vector[K-1] b;      // coefficients on family income
}
model{
    vector[K] p;
    vector[K] s;
    a ~ normal(0, 5);
    b ~ normal(0, 5);
    for ( i in 1:N ) {
        for ( j in 1:(K-1) ) s[j] = a[j] + b[j]*family_income[i];
        s[K] = 0;        
        p = softmax( s );
        career[i] ~ categorical( p );
    }
}
&quot;


stan_data <- list(
    N             = nrow(df),
    K             = 3,         
    career        = df$career,
    family_income = df$family_income
  )


m1 <- stan(model_code = stan_program, data = stan_data)
R 
m1

stan 2

R 
stan_program <- &quot;
data {
  int&lt;lower = 2&gt; K;
  int&lt;lower = 0&gt; N;
  int&lt;lower = 1&gt; D;
  int&lt;lower = 1, upper = K&gt; y[N];
  matrix[N, D] x;
}
transformed data {
  vector[D] zeros = rep_vector(0, D);
}
parameters {
  matrix[D, K - 1] beta_raw;
}
transformed parameters {
  matrix[D, K] beta;
  beta = append_col(beta_raw, zeros);
}
model {
  matrix[N, K] x_beta = x * beta;

  to_vector(beta_raw) ~ normal(0, 5);  

  for (n in 1:N)
    y[n] ~ categorical_logit(to_vector(x_beta[n]));
}
&quot;

stan_data <- list(
    N = nrow(df),
    K = 3,         
    D = 2,         
    y = df$career,
    x = model.matrix( ~1 + family_income, data = df)
  )

m2 <- stan(model_code = stan_program, data = stan_data)
R 
m2
R 
pacman::p_unload(pacman::p_loaded(), character.only = TRUE)