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Fit a Simplex Regression Model

Source: R/simplex_fit.R
simplex_fit.Rd

Fits a simplex regression model with logit link for the mean and log link for the dispersion parameter using maximum likelihood via BFGS.

Usage

simplex_fit(
  y,
  X,
  Z = NULL,
  start = NULL,
  control = list(maxit = 500, reltol = 1e-10)
)

Arguments

y

Numeric vector of responses in (0, 1).

X

Numeric matrix of covariates for the mean sub-model (including intercept column). Dimension n x p.

Z

Numeric matrix of covariates for the dispersion sub-model (including intercept column). Dimension n x q. If NULL, defaults to an intercept-only model (constant dispersion).

start

Optional numeric vector of starting values of length p + q. If NULL, OLS-based starting values are computed automatically.

control

A list passed to optim. Defaults to list(maxit = 500, reltol = 1e-10).

Value

A list of class "simplexfit" with components:

coefficients

Named numeric vector of MLE estimates (beta, gamma).

loglik

Log-likelihood at the MLE.

fitted.mu

Fitted means.

fitted.sigma2

Fitted dispersion values.

vcov.fisher

Variance-covariance matrix from Fisher information.

se

Standard errors.

converged

Logical; whether BFGS converged.

X

Design matrix for mean sub-model.

Z

Design matrix for dispersion sub-model.

y

Response vector.

n, p, q

Sample size and number of mean/dispersion parameters.

See also

simplex_gof, simplex_diag

Examples

data(ammonia)
X <- cbind(1, ammonia$corr_ar, ammonia$temp_agua,
           ammonia$corr_ar * ammonia$temp_agua)
Z <- cbind(1, ammonia$temp_agua,
           ammonia$corr_ar * ammonia$temp_agua)
fit <- simplex_fit(ammonia$perda, X, Z)
print(fit)
#> 
#> Simplex Regression  (n = 21 ; p = 4 ; q = 3 )
#> 
#>        Estimate Std.Error z.value      Pr
#> beta1  -12.9893    2.1038 -6.1742 < 0.001
#> beta2    0.1312    0.0363  3.6140 < 0.001
#> beta3    0.2705    0.1024  2.6408 0.00827
#> beta4   -0.0037    0.0017 -2.1473 0.03177
#> gamma1   3.8342    3.3908  1.1308 0.25815
#> gamma2  -0.4454    0.2882 -1.5456 0.12219
#> gamma3   0.0044    0.0024  1.8791 0.06024
#> 
#> Log-likelihood: 100.4159  |  converged: TRUE