# Summarize a 'misrepEM' Model Fit `summary` method for class 'misrepEM'. ```r ## S3 method for class 'misrepEM' summary(object, ...) ## S3 method for class 'summary.misrepEM' print(x, ...) ``` ## Arguments - `object`: an object of class "`misrepEM`", usually resulting from a call to one of `gammaRegMisrepEM`, `LnRegMisrepEM`, `NormRegMisrepEM`, `nbRegMisrepEM` or `poisRegMisrepEM`. - `x`: an object of class "`summary.misrepEM`", usually resulting from a call to `summary.misrepEM`. - ``...``: currently not used. ## Returns `summary.misrepEM` returns an object of class `"summary.misrepEM"`, a list of length 5 with the following components: - **coefficients**: a `data.frame` of coefficients, standard errors, standardized coefficients, two-tailed p-values corresponding to the standardized coefficient based on a Student-t or Normal reference distribution, and 'significance stars.' - **ICs**: a named numeric vector of length three, containing the Akaike Information Criterion (AIC), the corrected AIC (AICc) and the Bayesian Information Criterion (BIC). - **loglik**: numeric. The log-likelihood of the fitted `misrepEM` model. - **lambda**: numeric. The estimated prevalence of misrepresentation. - **lambda_stderror**: numeric. The standard error of the estimated prevalence of misrepresentation. ## References Xia, Michelle, Rexford Akakpo, and Matthew Albaugh. "Maximum Likelihood Approaches to Misrepresentation Models in GLM ratemaking: Model Comparisons." **Variance** 16.1 (2023). Akakpo, R. M., Xia, M., & Polansky, A. M. (2019). Frequentist inference in insurance ratemaking models adjusting for misrepresentation. **ASTIN Bulletin: The Journal of the IAA, 49**(1), 117-146. Xia, M., Hua, L., & Vadnais, G. (2018). Embedded predictive analysis of misrepresentation risk in GLM ratemaking models. **Variance, 12**(1), 39-58. ## Examples ```r # Simulate data n <- 2000 p0 <- 0.25 X1 <- rbinom(n, 1, 0.4) X2 <- rnorm(n, 0, 1) X3 <- rbeta(n, 2, 1) theta0 <- 0.3 V <- rbinom(n,1,theta0) V_star <- V V_star[V==1] <- rbinom(sum(V==1),1,1-p0) a0 <- 1 a1 <- 2 a2 <- 0 a3 <- 4 a4 <- 2 mu <- exp(a0 + a1*X1 + a2*X2 + a3*X3 + a4*V) phi <- 0.2 alpha0 <- 1/phi beta <- 1/mu/phi Y <- rgamma(n, alpha0, beta) data <- data.frame(Y = Y, X1 = X1, X2 = X2, X3 = X3, V_star = V_star) gamma_fit <- gammaRegMisrepEM(formula = Y ~ X1 + X2 + X3 + V_star, v_star = "V_star", data = data) summary(gamma_fit) # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) 1.00137 0.03413 29.33857 <2e-16 *** # X1 2.01388 0.02154 93.48440 <2e-16 *** # X2 -0.00193 0.01038 -0.18589 0.85255 # X3 4.00101 0.04560 87.74528 <2e-16 *** # V_star 2.00567 0.02240 89.54515 <2e-16 *** # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # --- # AIC AICc BIC # 23362.50 23362.56 23401.71 # --- # Log-Likelihood # -11674.25 # --- # Lambda: 0.09635239 std.err: 0.007641834 ```

summary.misrepEM function