# Print Summary Output This function prints a summary of the result object returned by the function `"lm"` for estimating linear regression models and for the result object returned by the function `"lmer"` from the `lme4` or `lmerTest` package, or by the function `"rlmer"` from the `robustlmm` package to estimate two- or three-level (robust) multilevel and linear mixed-effects models. By default, the function prints the function call, model summary, and the regression coefficient table. ```r summa(model, print = c("all", "default", "call", "descript", "cormat", "modsum", "coef", "confint", "stdcoef", "vif"), robust = FALSE, ddf = c("Satterthwaite", "Kenward-Roger", "lme4"), conf.level = 0.95, method = c("profile", "wald", "boot"), R = 1000, boot = c("perc", "basic", "norm"), seed = NULL, digits = 2, p.digits = 3, write = NULL, append = TRUE, check = TRUE, output = TRUE) ``` ## Arguments - `model`: a fitted model of class `"lm"`, `"lmerMod"`, `"rlmerMod"`, or `"lmerModLmerTest"` - `print`: a character vector indicating which results to print, i.e. `"all"`, for all results, `"call"` for the function call, `"descript"` for descriptive statistics, `cormat` for the Pearson product-moment correlation matrix for models estimated by `"lm"` (see `cor.matrix` function) or within- and between-group correlation matrix for models estimated by `"lmer"` (see `multilevel.cor` function), `modsum` for the multiple correlation, r-squared, and F-test for models estimated by `"lm"` or model summary, marginal, and conditional R-squared for models estimated by `"lmer"` (see `multilevel.r2` function), `coef` for the unstandardized coefficients for models estimated by `"lm"` or random effects and fixed effects for models estimated by `"lmer"`, `confint` for the confidence interval for unstandardized coefficients, `stdcoef` for the standardized coefficients (see `coeff.std function`), and `vif` for the variance inflation factor (see `check.collin` function). The default setting is `print = c("call", "modsum", "coef")`. Note that when a fitted model of class `"rlmerMod"` is specified for the argument `model`, the argument `print` is always `c("call", "coef")`, i.e., `"descript"`, `"cormat"`, `"modsum"`, `"confint"`, `"stdcoef"`, and `"vif"` are not available for an `"rlmerMod"` object. - `robust`: logical: if `TRUE`, heteroscedasticity-consistent standard errors, confidence intervals, and heteroscedasticity-robust F-test using the HC4 estimator are computed for linear models estimated by using the `lm()` function or cluster-robust standard errors using the CR2 estimator is computed for multilevel and linear mixed-effects models estimated by using the `lmer()` function (see `coeff.robust` function). - `ddf`: a character string for specifying the method for computing the degrees of freedom when using the `lmerTest` package to obtain **p**-values for fixed effects in multilevel and linear mixed-effects models, i.e., `"Satterthwaite"` (default) for Satterthwaite's method, `"Kenward-Roger"` for the Kenward-Roger's method, and `"lme4"` for the lme4-summary without degrees of freedom and significance values (see Kuznetsova et al., 2017). Note that when a fitted model of class `"rlmerMod"` is specified for the argument `model`, Satterthwaite or Kenward-Roger degrees of freedom are computed only if the R package `lmerTest` is loaded. - `conf.level`: a numeric value between 0 and 1 indicating the confidence level of the interval. - `method`: a character string for specifying the method for computing confidence intervals (CI), i.e., `"profile"` (default) for computing a likelihood profile and finding the appropriate cutoffs based on the likelihood ratio test, `"Wald"` for approximating the CIs based on the estimated local curvature of the likelihood surface, and `"boot"` for performing bootstrapping with CIs computed from the bootstrap distribution according to the argument `boot`. - `R`: a numeric value indicating the number of bootstrap replicates (default is 1000). - `boot`: a character string for specifying the type of bootstrap confidence intervals (CI), i.e., i.e., `"perc"` (default), for the percentile bootstrap CI, `"basic"` for the basic bootstrap CI, and `"norm"` for the normal approximation bootstrap CI. - `seed`: a numeric value specifying seeds of the pseudo-random numbers used in the bootstrap algorithm when conducting bootstrapping. - `digits`: an integer value indicating the number of decimal places to be used. - `p.digits`: an integer value indicating the number of decimal places to be used for displaying multiple R, R-squared and **p**-value. - `write`: a character string naming a file for writing the output into either a text file with file extension `".txt"` (e.g., `"Output.txt"`) or Excel file with file extension `".xlsx"` (e.g., `"Output.xlsx"`). If the file name does not contain any file extension, an Excel file will be written. - `append`: logical: if `TRUE` (default), output will be appended to an existing text file with extension `.txt` specified in `write`, if `FALSE` existing text file will be overwritten. - `check`: logical: if `TRUE` (default), argument specification is checked. - `output`: logical: if `TRUE` (default), output is shown on the console. ## Returns Returns an object of class `misty.object`, which is a list with following entries: - **`call`**: function call - **`type`**: type of analysis - **`model`**: model specified in `model` - **`args`**: specification of function arguments - **`result`**: list with results, i.e., `call` for the the function call, `descript` for descriptive statistics, `cormat` for the correlation matrix, `modsum` for the model summary, `randeff` for the variance and correlation components,`coef` for the model coefficients, `weights` for the robustness weights and `converg` for the convergence check, i.e., `1` = model converged, `0` = model singular, and `-1` model not converged. ## Details - **Robust Estimation of Multilevel and Linear Mixed-Effects Models**: The function `rlmer` from the `robustlmm` package does not provide any degrees of freedom or significance values. This function re-estimates the model without using robust estimation to obtain the Satterthwaite or Kenward-Roger degrees of freedom depending on the argument `ddf` before computing significance values for the regression coefficients based on parameter estimates and standard error of the robust multilevel mixed-effects (see Sleegers et al. (2021). ## Examples ```r #---------------------------------------------------------------------------- # Linear Model # Estimate linear model mod.lm <- lm(mpg ~ cyl + disp, data = mtcars) # Example 1a: Default setting summa(mod.lm) # Example 1b: Heteroscedasticity-consistent standard errors summa(mod.lm, robust = TRUE) # Example 1c: Print all available results summa(mod.lm, print = "all") # Example 1d: Print default results plus standardized coefficient summa(mod.lm, print = c("default", "stdcoef")) ## Not run: #---------------------------------------------------------------------------- # Multilevel and Linear Mixed-Effects Model # Load lme4 and misty package misty::libraries(lme4, misty) # Load data set "Demo.twolevel" in the lavaan package data("Demo.twolevel", package = "lavaan") #------------------ ## Two-Level Data # Cluster-mean centering, center() from the misty package Demo.twolevel <- center(Demo.twolevel, x2, type = "CWC", cluster = "cluster") # Grand-mean centering, center() from the misty package Demo.twolevel <- center(Demo.twolevel, w1, type = "CGM", cluster = "cluster") # Estimate two-level mixed-effects model mod.lmer2 <- lmer(y1 ~ x2.c + w1.c + x2.c:w1.c + (1 + x2.c | cluster), data = Demo.twolevel) # Example 2a: Default setting summa(mod.lmer2) # Example 2b: Print all available results summa(mod.lmer2, print = "all") # Example 2c: Print default results plus standardized coefficient summa(mod.lmer2, print = c("default", "stdcoef")) # Load lmerTest package library(lmerTest) # Re-estimate two-level model using the lme4 and lmerTest package mod.lmer2 <- lmer(y1 ~ x2.c + w1.c + x2.c:w1.c + (1 + x2.c | cluster), data = Demo.twolevel) # Example 2d: Default setting, Satterthwaite's method summa(mod.lmer2) # Example 2e: Kenward-Roger's method summa(mod.lmer2, ddf = "Kenward-Roger") # Example 2f: Cluster-robust standard errors summa(mod.lmer2, robust = TRUE) #------------------ ## Robust Estimation using the R package robustlmm # Estimate two-level mixed-effects model mod.lmer2r <- robustlmm::rlmer(y1 ~ x2.c + w1.c + x2.c:w1.c + (1 + x2.c | cluster), data = Demo.twolevel) # Example 2f: Default setting summa(mod.lmer2r) #------------------ ## Three-Level Data # Create arbitrary three-level data Demo.threelevel <- data.frame(Demo.twolevel, cluster2 = Demo.twolevel$cluster, cluster3 = rep(1:10, each = 250)) # Cluster-mean centering, center() from the misty package Demo.threelevel <- center(Demo.threelevel, x1, type = "CWC", cluster = c("cluster3", "cluster2")) # Cluster-mean centering, center() from the misty package Demo.threelevel <- center(Demo.threelevel, w1, type = "CWC", cluster = c("cluster3", "cluster2")) # Estimate three-level model using the lme4 package mod.lmer3 <- lmer(y1 ~ x1.c + w1.c + (1 | cluster3/cluster2), data = Demo.threelevel) # Example 3a: Default setting summa(mod.lmer3) # Example 3b: Print all available results summa(mod.lmer3, print = "all") #------------------ ## Robust Estimation using the R package robustlmm # Estimate three-level model using the lme4 package mod.lmer3r <- robustlmm::rlmer(y1 ~ x1.c + w1.c + (1 | cluster3/cluster2), data = Demo.threelevel) # Example 3c: Default setting summa(mod.lmer3r) #---------------------------------------------------------------------------- # Write Results # Example 4a: Write Results into a text file summa(mod.lm, print = "all", write = "Linear_Model.txt") # Example 4b: Write Results into a Excel file summa(mod.lm, print = "all", write = "Linear_Model.xlsx") ## End(Not run) ``` ## References Kuznetsova, A, Brockhoff, P. B., & Christensen, R. H. B. (2017). lmerTest Package: Tests in linear mixed effects models. **Journal of Statistical Software, 82** 13, 1-26. https://doi.org/10.18637/jss.v082.i13 Sleegers, W. W. A., Proulx, T., & van Beest, I. (2021). Pupillometry and hindsight bias: Physiological arousal predicts compensatory behavior. **Social Psychological and Personality Science, 12**(7), 1146–1154. https://doi.org/10.1177/1948550620966153 ## See Also `descript`, `cor.matrix`, `coeff.std`, `coeff.robust`, `check.collin` ## Author(s) Takuya Yanagida

summa function