Compute Absolute Fitted Values with Confidence Intervals, `calc_abs_fit_val`

Purpose

This function calculates absolute predicted values (fitted values) from regression models for specific covariate combinations, with accompanying confidence intervals. This is in contrast to the relative predicted values that are typically reported in regression model outputs.

Key Features

Works with any regression model family supported by car::deltaMethod() (gaussian, binomial, poisson… etc.)
Allows exponentiation of estimates for models with log-link functions
Computes Delta Method-based confidence intervals for the predicted values
Returns publication quality-formatted results with user-specified decimal precision

Mathematical Foundation

The function applies the Delta Method to compute: $\hat{y} = g(\hat{\beta})$ with variance: $\text{Var}(\hat{y}) = \nabla g(\hat{\beta})^T \cdot \text{Var}(\hat{\beta}) \cdot \nabla g(\hat{\beta})$ Where $g(\cdot)$ represents the linear combination of parameters specified in params.

Parameter Details

Parameter	Type	Description	Example
`model`	Regression object	Fitted model (lm, glm, etc.)	`lm(y ~ x1 + x2, data)`
`params`	Character string	Linear combination of parameters	`"(Intercept) + age50 + treatment1"`
`exp`	Logical	Exponentiate estimates (for log models)	`TRUE` for Poisson/logistic
`n_digits`	Integer	Decimal precision in output	`3` for 0.123

Example Applications

# Call function
source("https://raw.githubusercontent.com/Mohamed-Albirair/my-R-functions/refs/heads/main/R/regression/calc_abs_fit_val.R")

Example 1: Linear model, predict at specific values

# Fit regression model
linear_model <- lm(formula = salary ~ experience + education,
                   data    = salary_data)

# Run function
calc_abs_effect_val(
      model    = linear_model,
      params   = "(Intercept) + experience*10 + education*16",
      exp      = FALSE,
      n_digits = 2
)

Example 2: Logistic model, exponentiate to get odds

# Fit regression model
logistic_model <- glm(formula = disease ~ age + bmi,
                      data    = health_data,
                      family  = binomial)

# Run function
calc_abs_effect_val(
      model    = logistic_model,
      params   = "(Intercept) + age*45 + bmi*25",
      exp      = TRUE,  # Exponentiate log-odds to get odds
      n_digits = 4
)

Example 3: Poisson model, predict expected counts

# Fit regression model
poisson_model <- glm(formula = count ~ time + dose,
                     data    = count_data,
                     family  = poisson)

# Run function
calc_abs_effect_val(
      model    = poisson_model,
      params   = "(Intercept) + time*24 + dose*100",
      exp      = TRUE,  # Exponentiate log-rate to get rate
      n_digits = 1
)

Output Structure

The function returns a data frame with:

Estimate: Point prediction for the specified covariate combination
LCL: Lower 95% confidence limit
UCL: Upper 95% confidence limit

# Sample (raw) output:
#           Estimate   LCL   UCL
# Effect     125.430 110.2 140.7

Advanced Usage

Custom Standard Errors

# Use robust standard errors
calc_abs_effect_val(
      model  = your_model,
      params = "(Intercept) + x1*value1 + x2*value2",
      exp    = FALSE
)
# The function automatically uses vcov(model) - replace with sandwich::vcovHC() if needed

Multiple Contrasts

# Compute predictions for several scenarios
scenarios <- list(
      "Young_Low" = "(Intercept) + age*30 + bmi*22",
      "Old_High"  = "(Intercept) + age*65 + bmi*32"
)

lapply(scenarios, function(p) {
      calc_abs_effect_val(model = model, params = p, exp = TRUE)
})

Technical Notes

Method: Uses the Delta Method via car::deltaMethod() for variance estimation
Assumptions: Requires model to have a vcov() method and support from car::deltaMethod()
Limitations: Delta Method assumes asymptotic normality; may be less accurate with small samples
Alternatives: For non-linear combinations, consider simulation-based methods

Compute Absolute Fitted Values with Confidence Intervals, calc_abs_fit_val