# Help with reduce_sum - hierarchical logistic regression

I am trying to convert the following model code to a multithreaded format using reduce_sum

Original:

data {
int<lower=0> N;//Number of observations
int<lower=1> J;//Number of predictors with random slope
int<lower=1> K;//Number of predictors with non-random slope
int<lower=1> L;//Number of customers/groups
int<lower=0,upper=1> y[N];//Binary response variable
int<lower=1,upper=L> ll[N];//Number of observations in groups
matrix[N,K] x1;
matrix[N,J] x2;
}
parameters {
vector[J] rbeta_mu; //mean of distribution of beta parameters
vector<lower=0>[J] rbeta_sigma; //variance of distribution of beta parameters
vector[J] beta_raw[L]; //group-specific parameters beta
vector[K] beta;
}
transformed parameters {
vector[J] rbeta[L];
for (l in 1:L)
for (j in 1:J)
rbeta[l][j] = rbeta_mu[j] + rbeta_sigma[j] * beta_raw[l][j]; // coefficients on x
}
model {
rbeta_mu ~ normal(0,100);
rbeta_sigma ~ cauchy(0,10);
beta~normal(0,10);
for (l in 1:L)
beta_raw[l] ~ normal(0,1);

for(n in 1:N)
y[n]~bernoulli_logit(x1[n] * beta + x2[n] * rbeta[ll[n]]);
}

Reduce_Sum attempt :

functions {
real partial_sum(int start,
int end,
int[] y_slice,
matrix x1,
matrix x2,
vector[] beta,
matrix rbeta,
int J,
int[] ll) {

return bernoulli_logit_lpmf(y_slice[start:end] | x1[start:end,] * beta + (x2[start:end,:] .* rbeta[ll[start:end],:]) * rep_vector(1,J));
}
}
data {
int<lower=0> N;//Number of observations
int<lower=1> J;//Number of predictors with random slope
int<lower=1> K;//Number of predictors with non-random slope
int<lower=1> L;//Number of customers/groups
int<lower=0,upper=1> y[N];//Binary response variable
int<lower=1,upper=L> ll[N];//Number of observations in groups
matrix[N,K] x1;
matrix[N,J] x2;
}
parameters {
vector[J] rbeta_mu; //mean of distribution of beta parameters
vector<lower=0>[J] rbeta_sigma; //variance of distribution of beta parameters
vector[J] beta_raw[L]; //group-specific parameters beta
vector[K] beta;
}
transformed parameters {
vector[J] rbeta[L];
for (l in 1:L)
for (j in 1:J)
rbeta[l][j] = rbeta_mu[j] + rbeta_sigma[j] * beta_raw[l][j]; // coefficients on x
}
model {
rbeta_mu ~ normal(0,100);
rbeta_sigma ~ cauchy(0,10);
beta~normal(0,10);
for (l in 1:L)
beta_raw[l] ~ normal(0,1);
target+=reduce_sum(partial_sum,1,y,x1,x2,beta,rbeta,J,ll);
}

I am getting the following error:

This is the statement giving the error:

return bernoulli_logit_lpmf(y_slice[start:end] | x1[start:end,] * beta + (x2[start:end,:] .* rbeta[ll[start:end],:]) * rep_vector(1,J));

Any help on how to resolve it is greatly appreciated.

The error message seems a bit weird, but there is at least one error I am seeing:

x2[start:end,:] .* rbeta[ll[start:end],:]

The problem is that:

• x2[start:end, :] is a matrix
• rbeta[ll[start:end],:] is an array of vector

The product of these 2 types is not defined.
Its not really evident what is desired here, but I am guessing elementwise products of matrix rows and vectors? If so, that has to be done with a loop.

What if rbeta was a matrix :

functions {
real partial_sum(int start,
int end,
int[] y_slice,
matrix x1,
matrix x2,
vector[] beta,
matrix rbeta,
int J,
int[] ll) {

return bernoulli_logit_lpmf(y_slice[start:end] | x1[start:end,] * beta + (x2[start:end,:] .* rbeta[ll[start:end],:]) * rep_vector(1,J));
}
}
data {
int<lower=0> N;//Number of observations
int<lower=1> J;//Number of predictors with random slope
int<lower=1> K;//Number of predictors with non-random slope
int<lower=1> L;//Number of customers/groups
int<lower=0,upper=1> y[N];//Binary response variable
int<lower=1,upper=L> ll[N];//Number of observations in groups
matrix[N,K] x1;
matrix[N,J] x2;
}
parameters {
vector[J] rbeta_mu; //mean of distribution of beta parameters
vector<lower=0>[J] rbeta_sigma; //variance of distribution of beta parameters
vector[J] beta_raw[L]; //group-specific parameters beta
vector[K] beta;
}
transformed parameters {
matrix[L,J] rbeta;
for (l in 1:L)
rbeta[l] = rbeta_mu + rbeta_sigma .* beta_raw[l]; // coefficients on x
}
model {
rbeta_mu ~ normal(0,100);
rbeta_sigma ~ cauchy(0,10);
beta~normal(0,10);
for (l in 1:L)
beta_raw[l] ~ normal(0,1);
target+=reduce_sum(partial_sum,1,y,x1,x2,beta,rbeta,J,ll);
}

@rok_cesnovar even upon converting rbeta to matrix it does not help.

@rok_cesnovar

Upon just adding some brackets the error now changes position :

Before:

After:

The only difference between the two is the paranthesis around x1[start:end,:] * beta nothing else and here this should be possible.

A Bernoulli logit is not a good candidate for reduce_sum is what I would expect… but you can try.

In any case, maybe you consider to rewrite your model using the R package brms. Then you can just turn on a switch with brm for threading. Have a look for the vignette on threading within brms.