Hi all,

Thanks to those who assisted me in estimating a multinomial logit model. I am familiar with the interpretation of these coefficients in the conventional fashion in which a category of the outcome is left out. For this analysis, I unclear what the regression coefficients are conveying. The model is very simple, with a 4 category outcome and a dichotomous predictor (male/female). Here is the code

```
modelString <- "
data {
int <lower=2> K; // This is 4, the number of outcomes categories
int <lower=0> N;
int <lower=1> D; // This is the number of columns in the design matrix: 2
int <lower = 1, upper = K> ASBR07A[N];
matrix[N, D] x; // This will be N by 4 matrix of data
}
parameters {
matrix[D, K] beta; // This is a 2 x 4 matrix of betas
}
transformed parameters {
matrix[N, K] x_beta = x * beta; // N x 2 * 2 x 4
}
model {
to_vector(beta) ~ normal(0, 5);
for (i in 1:N)
ASBR07A[i] ~ categorical_logit(x_beta[i]');
}
generated quantities {
int<lower=1,upper=K> ASBR07A_rep[N];
for (i in 1:N){
ASBR07A_rep[i] = categorical_logit_rng(x_beta[i]');
}
}
"
```

and here is the output.

```
Inference for Stan model: 439376e657c9f05511f724d396ba31c0.
1 chains, each with iter=10000; warmup=5000; thin=10;
post-warmup draws per chain=500, total post-warmup draws=500.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta[1,1] 0.20 0.11 2.51 -4.21 -1.58 0.16 1.85 5.32 497 1
beta[1,2] 0.06 0.11 2.51 -4.32 -1.74 0.03 1.72 5.14 500 1
beta[1,3] -0.28 0.11 2.52 -4.79 -2.10 -0.31 1.37 4.99 501 1
beta[1,4] -0.27 0.11 2.51 -4.59 -2.08 -0.31 1.44 4.98 496 1
beta[2,1] 0.58 0.11 2.47 -4.24 -1.04 0.69 2.23 5.33 485 1
beta[2,2] 0.07 0.11 2.48 -4.73 -1.56 0.21 1.66 4.92 486 1
beta[2,3] -0.22 0.11 2.47 -5.12 -1.80 0.00 1.37 4.54 478 1
beta[2,4] -0.14 0.11 2.47 -5.00 -1.78 0.06 1.45 4.49 481 1
Samples were drawn using NUTS(diag_e) at Tue Nov 10 21:42:29 2020.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
```

So for example, what does is beta[1,1,] telling me?

Thanks in advance.