This methods performs comparisons of lm-objects and creates formatted character
strings and a model comparison table to report the results in accordance with APA manuscript guidelines.
apa_print.list(x, anova_fun = stats::anova, ci = 0.9,
boot_samples = 10000, observed_predictors = TRUE, in_paren = FALSE,
...)List. List containing to be compared lm-objects. If the list is completely named, element names are used as model names in the output object.
Function. Function to compare model-objects contained in x.
Numeric. Confidence level for the bootstrap confidence interval for \(\Delta R^2\) (range [0, 1]); ignored if boot_samples = 0.
Numeric. Number of bootstrap samples to estimate confidence intervals for \(\Delta R^2\).
Logical. Indicates whether predictor variables were observed. See details.
Logical. Indicates if the formated string will be reported inside parentheses. See details.
Additional arguments passed to anova_fun
apa_print.list returns a named list containing the following components according to the input:
statisticA named list of character strings giving the test statistic, parameters, and p value for each non-baseline model.
estimateA named list of character strings giving the effect size estimates for each non-baseline model
full_resultA named list of character strings comprised of estimate and statistic for each non-baseline model
tableA data.frame containing the complete model comparison table including regression coefficients, which can be passed to apa_table.
As demonstrated by Algina, Keselman & Penfield (2007), asymptotic confidence intervals for \(\Delta R^2\)
are often unreliable. Confidence intervals for model comparisons of lm-objects are, therefore, estimated
using their modified percentile bootstrap method. Note that the accuracy of the confidence intervals depends on
the number of predictors \(p\), their distribution, and the sample size \(n\):
"When the predictor distribution is multivariate normal, one can obtain accurate CIs for \(\rho^2\) with \(n \geq~50\) when \(p = 3\). For \(p = 6\) and for \(p = 9\), \(n \geq~100\) is advisable. When the predictor distribution is nonnormal in form, sample size requirements vary with type of nonnormality." (p. 939, Algina, Keselman & Penfield, 2010)
If MBESS is available, confidence intervals for \(R^2\) are computed using ci.R2 to
obtain a confidence region that corresponds to the confidence level ci, the default being a 90% CI (see
Steiger, 2004). If observed_predictors = FALSE, it is assumed that predictors are fixed variables, i.e.,
"the values of the [predictors] were selected a priori as part of the research design" (p. 15, Kelly, 2007);
put differently, it is assumed that predictors are not random. The confidence intervals for the regression
coefficients in the model comparison table correspond to the \(\alpha\)-level chosen for \(R^2\) and
\(\Delta R^2\) (e.g., 90% CI or \(\alpha = 0.10\) for \(R^2\) and \(\Delta R^2\) yields a 95% CI for
regression coefficients, Steiger, 2004).
If in_paren is TRUE parentheses in the formatted string, such as those surrounding degrees
of freedom, are replaced with brackets.
Algina, J., Keselman, H. J., & Penfield, R. D. (2007). Confidence Intervals for an Effect Size Measure in Multiple Linear Regression. Educational and Psychological Measurement, 67(2), 207--218. doi:10.1177/0013164406292030
Algina, J., Keselman, H. J., & Penfield, R. D. (2010). Confidence Intervals for Squared Semipartial Correlation Coefficients: The Effect of Nonnormality. Educational and Psychological Measurement, 70(6), 926--940. doi:10.1177/0013164410379335
Steiger (2004). Beyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis. Psychological Methods, 9(2), 164-182. doi:10.1037/1082-989X.9.2.164
Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1-24. doi:10.18637/jss.v020.i08
Other apa_print: apa_print.BFBayesFactor,
apa_print.aov,
apa_print.emmGrid,
apa_print.glht,
apa_print.glm,
apa_print.htest, apa_print
# NOT RUN {
mod1 <- lm(Sepal.Length ~ Sepal.Width, data = iris)
mod2 <- update(mod1, formula = . ~ . + Petal.Length)
mod3 <- update(mod2, formula = . ~ . + Petal.Width)
# No bootstrapped Delta R^2 CI
apa_print(list(Baseline = mod1, Length = mod2, Both = mod3), boot_samples = 0)
# }
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