# Specified Approximation Method This function determines when a specific path in a Structural Equation Modeling (SEM) model changes sign by iteratively removing most influential data points (determined by naive method) and outputs relevant results. Use method 3 - Specified Approximation Method. ```r Test3( df, model, var_one, var_two, PAR, threshold, fit, estimates, conc, int, par_value, max_final, N, signFactor, equalCons = 0L, calcMeth = "Hessian", ... ) ``` ## Arguments - `df`: A data frame containing the dataset. - `model`: A specified SEM model. - `var_one`: The first variable of interest. - `var_two`: The second variable of interest. - `PAR`: The path of interest. - `threshold`: The threshold for percentage of data dropped. - `fit`: The SEM object. - `estimates`: The estimates from the SEM model. - `conc`: A data frame containing the parameter of interest. - `int`: The value of the path of interest. - `par_value`: The original value of the parameter of interest. - `max_final`: The maximum number of influential data points to consider. - `N`: The total number of data points. - `signFactor`: A factor indicating the direction of parameter change (positive or negative). - `equalCons`: The equality constraint used in the SEM model (default is 0). - `calcMeth`: The method used for approximation (default is 'Hessian'). - `...`: Other arguments. ## Returns A list of class `TestResult3` containing: - **methodname**: The name of the method used. - **testindex**: The index of the test performed. - **max_drops**: The maximum number of data points dropped. - **est_diff**: The expected change in parameter value. - **act_diff**: The actual change in parameter value. - **final_par_value**: The parameter value after dropping the influential points. - **initial_par_value**: The original parameter value. - **sign_switch_possible**: Logical indicating whether it was possible to change the sign of the parameter. - **dropped_points**: The indices of the most influential data points. ## Examples ```r library(lavaan) library(dplyr) library(semfindr) library(R.utils) # Import data df <- PoliticalDemocracy # Build Model model <- ' # measurement model ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' var_one <- 'dem65' # first term var_two <- 'ind60' # second term PAR <- c("dem65~ind60") # full relation threshold <- 10 # Fit SEM model fit <- lavaan::sem(model, data = df) summary(fit) # Get Estimates of Parameters from SEM estimates <- parameterEstimates(fit) # Determine The Value of The Parameter of Interest conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est) int <- conc %>% filter(lhs == var_one & rhs == var_two) par_value <- int$est # this is the value of the parameter of interest # Compute max number of points to be dropped max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary N <- nrow(df) # store number of observations in df for convenience # Determine whether parameter is negative or positive in order # to assess which direction to perturb it signFactor <- ifelse(par_value >= 0L, TRUE, FALSE) Test3_result = Test3(df, model, var_one, var_two, PAR, threshold, fit, estimates, conc, int, par_value, max_final, N, signFactor,equalCons = 0L) summary(Test3_result) ```

Test3 function