# Make products of indicators using no centering, mean centering, double-mean centering, or residual centering The `indProd` function will make products of indicators using no centering, mean centering, double-mean centering, or residual centering. The `orthogonalize` function is the shortcut of the `indProd` function to make the residual-centered indicators products. ```r indProd(data, var1, var2, var3 = NULL, match = TRUE, meanC = TRUE, residualC = FALSE, doubleMC = TRUE, namesProd = NULL) orthogonalize(data, var1, var2, var3 = NULL, match = TRUE, namesProd = NULL) ``` ## Arguments - `data`: The desired data to be transformed. - `var1`: Names or indices of the variables loaded on the first factor - `var2`: Names or indices of the variables loaded on the second factor - `var3`: Names or indices of the variables loaded on the third factor (for three-way interaction) - `match`: Specify `TRUE` to use match-paired approach (Marsh, Wen, & Hau, 2004). If `FALSE`, the resulting products are all possible products. - `meanC`: Specify `TRUE` for mean centering the main effect indicator before making the products - `residualC`: Specify `TRUE` for residual centering the products by the main effect indicators (Little, Bovaird, & Widaman, 2006). - `doubleMC`: Specify `TRUE` for centering the resulting products (Lin et. al., 2010) - `namesProd`: The names of resulting products ## Returns The original data attached with the products. ## Examples ```r ## Mean centering / two-way interaction / match-paired dat <- indProd(attitude[ , -1], var1 = 1:3, var2 = 4:6) ## Residual centering / two-way interaction / match-paired dat2 <- indProd(attitude[ , -1], var1 = 1:3, var2 = 4:6, match = FALSE, meanC = FALSE, residualC = TRUE, doubleMC = FALSE) ## Double-mean centering / two-way interaction / match-paired dat3 <- indProd(attitude[ , -1], var1 = 1:3, var2 = 4:6, match = FALSE, meanC = TRUE, residualC = FALSE, doubleMC = TRUE) ## Mean centering / three-way interaction / match-paired dat4 <- indProd(attitude[ , -1], var1 = 1:2, var2 = 3:4, var3 = 5:6) ## Residual centering / three-way interaction / match-paired dat5 <- orthogonalize(attitude[ , -1], var1 = 1:2, var2 = 3:4, var3 = 5:6, match = FALSE) ## Double-mean centering / three-way interaction / match-paired dat6 <- indProd(attitude[ , -1], var1 = 1:2, var2 = 3:4, var3 = 5:6, match = FALSE, meanC = TRUE, residualC = TRUE, doubleMC = TRUE) ## To add product-indicators to multiple-imputed data sets HSMiss <- HolzingerSwineford1939[ , c(paste0("x", 1:9), "ageyr","agemo")] set.seed(12345) HSMiss$x5 <- ifelse(HSMiss$x5 <= quantile(HSMiss$x5, .3), NA, HSMiss$x5) age <- HSMiss$ageyr + HSMiss$agemo/12 HSMiss$x9 <- ifelse(age <= quantile(age, .3), NA, HSMiss$x9) library(Amelia) set.seed(12345) HS.amelia <- amelia(HSMiss, m = 3, p2s = FALSE) imps <- HS.amelia$imputations # extract a list of imputations ## apply indProd() to the list of data.frames imps2 <- lapply(imps, indProd, var1 = c("x1","x2","x3"), var2 = c("x4","x5","x6")) ## verify: lapply(imps2, head) ``` ## References Marsh, H. W., Wen, Z. & Hau, K. T. (2004). Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. **Psychological Methods, 9**(3), 275--300. tools:::Rd_expr_doi("10.1037/1082-989X.9.3.275") Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). Structural equation models of latent interactions: Clarification of orthogonalizing and double-mean-centering strategies. **Structural Equation Modeling, 17**(3), 374--391. tools:::Rd_expr_doi("10.1080/10705511.2010.488999") Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables. **Structural Equation Modeling, 13**(4), 497--519. tools:::Rd_expr_doi("10.1207/s15328007sem1304_1") ## See Also * `probe2WayMC()` For probing the two-way latent interaction when the results are obtained from mean-centering, or double-mean centering. * `probe3WayMC()` For probing the three-way latent interaction when the results are obtained from mean-centering, or double-mean centering. * `probe2WayRC()` For probing the two-way latent interaction when the results are obtained from residual-centering approach. * `probe3WayRC()` For probing the two-way latent interaction when the results are obtained from residual-centering approach. * `plotProbe()` Plot the simple intercepts and slopes of the latent interaction. ## Author(s) Sunthud Pornprasertmanit (psunthud@gmail.com ) Alexander Schoemann (East Carolina University; schoemanna@ecu.edu )

indProd function