Estimating equation for regression

Returns a p-by-n matrix of estimating equation contributions for regression models. Supports linear, logistic, and Poisson regression: $$\psi_i(\theta) = \{Y_i - g(X_i^T \theta)\} X_i$$

Usage

ee_regression(theta, X, y, model, weights = NULL, offset = NULL)

Arguments

theta

Numeric vector of length p (number of covariates).

X

Numeric n-by-p design matrix.

y

Numeric vector of n observed outcome values.

model

Character string: "linear", "logistic", or "poisson".

weights

Optional numeric vector of n weights. Default NULL.

offset

Optional numeric vector of n offsets. Default NULL.

Value

A p-by-n matrix.

Examples

fit <- m_estimate(
  mpg ~ wt + hp,
  data = mtcars,
  .ee = ee_regression,
  model = "linear"
)
summary(fit)
#> ── MEstimator Results ──────────────────────────────────────────────────────────
#> Observations: 32
#> Parameters: 3
#> 
#>               Estimate    Std.Err    Z-score    95% LCL    95% UCL    P-value    S-value
#> (Intercept)    37.2273     1.9389    19.2000    33.4271    41.0275     <2e-16   270.5102
#> wt             -3.8778     0.6199    -6.2553    -5.0929    -2.6628   3.97e-10    31.2310
#> hp             -0.0318     0.0066    -4.7807    -0.0448    -0.0187   1.75e-06    19.1270

# The same equation fits a logistic regression through the model argument.
fit_logit <- m_estimate(
  vs ~ mpg,
  data = mtcars,
  .ee = ee_regression,
  model = "logistic"
)
coef(fit_logit)
#> (Intercept)         mpg 
#>  -8.8330726   0.4304135