Fast Weighted Negative Binomial Regression, Estimate Only (C++ Backend)

Fits the same mean/dispersion-parameterized negative-binomial regression as fast_neg_bin_cpp (see that page, and fast_dnbinom_mu_vec_cpp, for the full model), with each observation's contribution to the log-likelihood multiplied by a nonnegative row weight weights[i]. Setting all weights to 1 recovers fast_neg_bin_cpp exactly.

Usage

fast_neg_bin_weighted_cpp(
  X,
  y,
  weights,
  warm_start_params = NULL,
  smart_cold_start = FALSE,
  maxit = 1000L,
  eps_f = 1e-08,
  eps_g = 1e-06,
  fixed_idx = NULL,
  fixed_values = NULL,
  optimization_alg = "lbfgs",
  warm_start_fisher_info = NULL,
  estimate_only = FALSE
)

Arguments

X

A numeric matrix of predictors, \(n \times p\).

y

A numeric (integer-valued) vector of non-negative observed counts, length \(n\).

weights

A nonnegative numeric vector of length \(n\) giving each row's weight.

warm_start_params

Optional starting values for coefficients and dispersion. If provided, smart_cold_start is ignored.

smart_cold_start

Logical. If TRUE, use an initial OLS-based guess when starting from scratch (a "cold start") with no prior knowledge. This is ignored if a warm start is provided.

maxit

Maximum number of optimizer iterations.

eps_f

Convergence tolerance on the objective (log-likelihood) value.

eps_g

Convergence tolerance on the gradient norm.

fixed_idx

Optional integer indices (into the c(beta, log(theta)) parameter layout) of parameters to hold fixed rather than estimate.

fixed_values

Optional values to fix the parameters named by fixed_idx at.

optimization_alg

Optimization algorithm: "lbfgs" (default) or "newton_raphson".

warm_start_fisher_info

Optional initial Fisher Information matrix to warm-start curvature information.

estimate_only

If TRUE, skip Fisher information calculation.

Value

A list with the same components as fast_neg_bin_cpp: b, theta_hat, logLik, converged, iterations, and fisher_information (all reflecting the weighted log-likelihood).

See also

fast_neg_bin_cpp for the unweighted model and full documentation.

Examples

X = matrix(rnorm(100), 10, 10)
y = rpois(10, 2)
fast_neg_bin_weighted_cpp(X, y, weights = rep(1, 10))
#> $b
#>  [1] -1.10096439  0.12306130  0.55943200 -2.03947942 -0.45032432  0.11545561
#>  [7]  1.74134954  0.05038336 -0.64198342 -0.33597138
#> 
#> $theta_hat
#> [1] 3128.529
#> 
#> $logLik
#> [1] -9.861803
#> 
#> $converged
#> [1] TRUE
#> 
#> $num_iter
#> [1] 23
#> 
#> $hit_iteration_cap
#> [1] FALSE
#> 
#> $gradient_norm
#> [1] 0.01118875
#> 
#> $min_eigenvalue_information
#> [1] NaN
#> 
#> $dispersion_at_poisson_boundary
#> [1] FALSE
#> 
#> $fisher_information
#>                [,1]          [,2]          [,3]          [,4]          [,5]
#>  [1,]  5.828969e+00 -3.266424e-01  2.876450e+00  4.309775e-01 -0.5423488444
#>  [2,] -3.266424e-01  1.378805e+01  8.518026e+00  6.407435e+00  2.2488516937
#>  [3,]  2.876450e+00  8.518026e+00  1.119727e+01  6.089860e+00  0.4144641985
#>  [4,]  4.309775e-01  6.407435e+00  6.089860e+00  1.726406e+01 -7.1343704016
#>  [5,] -5.423488e-01  2.248852e+00  4.144642e-01 -7.134370e+00  9.0521717031
#>  [6,]  2.099621e+00 -1.254233e+01 -1.077706e+01 -5.509771e+00 -1.6630103548
#>  [7,] -7.496441e-02  6.718588e+00  2.733905e+00  2.304582e+00  3.3765919014
#>  [8,]  2.367642e+00 -5.267058e-01 -8.062256e+00 -1.277380e+01  7.2618579931
#>  [9,] -4.383028e-02  9.761803e+00  6.520752e+00 -6.535270e+00 11.7038268423
#> [10,] -3.194227e+00  5.269948e-01 -2.393151e+00 -1.185877e+01  4.8554236114
#> [11,] -2.634218e-05  2.091622e-05 -4.606250e-05 -2.914089e-04  0.0002916585
#>                [,6]         [,7]          [,8]          [,9]         [,10]
#>  [1,]  2.099621e+00 -0.074964408  2.367642e+00 -0.0438302789 -3.194227e+00
#>  [2,] -1.254233e+01  6.718587681 -5.267058e-01  9.7618033662  5.269948e-01
#>  [3,] -1.077706e+01  2.733905189 -8.062256e+00  6.5207520002 -2.393151e+00
#>  [4,] -5.509771e+00  2.304582144 -1.277380e+01 -6.5352701013 -1.185877e+01
#>  [5,] -1.663010e+00  3.376591901  7.261858e+00 11.7038268423  4.855424e+00
#>  [6,]  1.957045e+01 -3.671843732  6.191629e+00 -6.8846969722 -6.470383e-01
#>  [7,] -3.671844e+00  9.425941560  9.126470e+00  5.7772940487  6.937392e+00
#>  [8,]  6.191629e+00  9.126469884  3.569315e+01  3.3806070299  1.597892e+01
#>  [9,] -6.884697e+00  5.777294049  3.380607e+00 22.6824670051  7.425844e+00
#> [10,] -6.470383e-01  6.937391909  1.597892e+01  7.4258440589  2.576703e+01
#> [11,] -9.208585e-05  0.000290825  6.570469e-04  0.0001960197  4.447344e-04
#>               [,11]
#>  [1,] -2.634218e-05
#>  [2,]  2.091622e-05
#>  [3,] -4.606250e-05
#>  [4,] -2.914089e-04
#>  [5,]  2.916585e-04
#>  [6,] -9.208585e-05
#>  [7,]  2.908250e-04
#>  [8,]  6.570469e-04
#>  [9,]  1.960197e-04
#> [10,]  4.447344e-04
#> [11,]  2.693209e-03
#>