Confidence intervals for fitted categorical AD models

Computes Wald-based confidence intervals for the transition probability parameters of a fitted categorical antedependence model.

Usage

ci_cat(fit, y = NULL, level = 0.95, parameters = "all")

Arguments

fit: A fitted model object of class "cat_fit" from fit_cat().
y: Optional data matrix. If NULL, fit$cell_counts is used (observed counts for closed-form fits; expected counts for EM fits).
level: Confidence level (default 0.95).
parameters: Which parameters to compute CIs for: "all" (default), "marginal", or "transition".

Value

A list of class "cat_ci" containing:

marginal: Data frame of CIs for marginal parameters (if requested)
transition: List of data frames of CIs for transition parameters (if requested)
level: Confidence level used
settings: Model settings from fit

Details

Confidence intervals are computed using the Wald method based on the asymptotic normality of maximum likelihood estimators.

For a probability estimate $\hat{\pi}$ based on count N, the standard error is: $$SE(\hat{\pi}) = \sqrt{\frac{\hat{\pi}(1-\hat{\pi})}{N}}$$

For conditional probabilities $\hat{\pi}_{j|i}$ based on conditioning count $N_i$, the standard error is: $$SE(\hat{\pi}_{j|i}) = \sqrt{\frac{\hat{\pi}_{j|i}(1-\hat{\pi}_{j|i})}{N_i}}$$

The confidence interval is then: $$\hat{\pi} \pm z_{\alpha/2} \times SE(\hat{\pi})$$

Note: CIs are truncated to the interval from 0 to 1 when they exceed these bounds.

Missing-data fits with na_action = "marginalize" are not currently supported because observed cell counts are not stored for that path.

References

Agresti, A. (2013). Categorical Data Analysis (3rd ed.). Wiley.

Examples

if (FALSE) { # \dontrun{
# Fit a model
set.seed(123)
y <- simulate_cat(200, 5, order = 1, n_categories = 2)
fit <- fit_cat(y, order = 1)

# Compute confidence intervals
ci <- ci_cat(fit)
print(ci)

# Just marginal CIs
ci_marg <- ci_cat(fit, parameters = "marginal")
} # }