| Title: | Knock Errors Off Nice Guesses |
|---|---|
| Description: | Miscellaneous functions and data used in Qingyao's psychological research and teaching. Keng currently has a built-in dataset depress, and could (1) scale a vector, (2) test the significance and compute the cut-off values of Pearson's r without raw data, (3) compare lm()'s fitted outputs using R-squared, f_squared, post-hoc power, and PRE (Proportional Reduction in Error, also called partial R-squared or partial Eta-squared). (4) Calculate PRE from partial correlation, Cohen's f, or f_squared. (5) Compute the post-hoc power for one or a set of predictors in regression analysis without raw data, (6) Plan the sample size for one or a set of predictors in regression analysis. |
| Authors: | Qingyao Zhang [aut, cre] |
| Maintainer: | Qingyao Zhang <[email protected]> |
| License: | CC BY 4.0 |
| Version: | 2024.11.25 |
| Built: | 2024-11-24 20:22:05 UTC |
| Source: | https://github.com/qyaozh/keng |
Calculate PRE from Cohen's f, f_squared, or partial correlation
calc_PRE(f = NULL, f_squared = NULL, r_p = NULL)calc_PRE(f = NULL, f_squared = NULL, r_p = NULL)
f |
Cohen's f. Cohen (1988) suggested >=0.1, >=0.25, and >=0.40 as cut-off values of f for small, medium, and large effect sizes, respectively. |
f_squared |
Cohen's f_squared. Cohen (1988) suggested >=0.02, >=0.15, and >=0.35 as cut-off values of f for small, medium, and large effect sizes, respectively. |
r_p |
Partial correlation. |
A list including PRE, r_p (partial correlation), Cohen's f_squared, and f.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
calc_PRE(f = 0.1) calc_PRE(f_squared = 0.02) calc_PRE(r_p = 0.2)calc_PRE(f = 0.1) calc_PRE(f_squared = 0.02) calc_PRE(r_p = 0.2)
Compare lm()'s fitted outputs using PRE and R-squared.
compare_lm( fitC = NULL, fitA = NULL, n = NULL, PC = NULL, PA = NULL, SSEC = NULL, SSEA = NULL )compare_lm( fitC = NULL, fitA = NULL, n = NULL, PC = NULL, PA = NULL, SSEC = NULL, SSEA = NULL )
fitC |
The result of |
fitA |
The result of |
n |
Sample size of the model C or model A. model C and model A must use the same sample, and hence have the same sample size. |
PC |
The number of parameters in model C. |
PA |
The number of parameters in model A. PA must be larger than PC. |
SSEC |
The Sum of Squared Errors (SSE) of model C. |
SSEA |
The Sum of Squared Errors of model A. |
compare_lm() compare model A with model C using PRE (Proportional Reduction in Error) , R-squared, f_squared, and post-hoc power.
PRE is partial R-squared (called partial Eta-squared in Anova).
There are two ways of using compare_lm().
The first is giving compare_lm() fitC and fitA.
The second is giving n, PC, PA, SSEC, and SSEA.
The first way is more convenient, and it minimizes precision loss by omitting copying-and-pasting.
Note that the F-tests for PRE and that for R-squared change are equivalent.
Please refer to Judd et al. (2017) for more details about PRE, and refer to Aberson (2019) for more details about f_squared and post-hoc power.
A matrix with 11 rows and 4 columns. The first column reports information for baseline model (intercept-only model). the second for model C, the third for model A, and the fourth for the change (model A vs. model C). SSE (Sum of Squared Errors) and df of SSE for baseline model, model C, model A, and change (model A vs. model C) are reported in row 1 and row 2. The information in the fourth column are all for the change; put differently, These results could quantify the effect of one or a set of new parameters model A has but model C doesn't. If fitC and fitA are not inferior to the intercept-only model, R-squared, Adjusted R-squared, PRE, PRE_adjusted, and f_squared for the full model (compared with the baseline model) are reported for model C and model A. If model C or model A has at least one predictor, F -test with p, and post-hoc power would be computed for the corresponding full model.
Aberson, C. L. (2019). Applied power analysis for the behavioral sciences. Routledge.
Judd, C. M., McClelland, G. H., & Ryan, C. S. (2017). Data analysis: A model Comparison approach to regression, ANOVA, and beyond. Routledge.
x1 <- rnorm(193) x2 <- rnorm(193) y <- 0.3 + 0.2*x1 + 0.1*x2 + rnorm(193) dat <- data.frame(y, x1, x2) # Fix intercept to constant 1 using I(). fit1 <- lm(I(y - 1) ~ 0, dat) # Free intercept. fit2 <- lm(y ~ 1, dat) compare_lm(fit1, fit2) # One predictor. fit3 <- lm(y ~ x1, dat) compare_lm(fit2, fit3) # Fix intercept to 0.3 using offset(). intercept <- rep(0.3, 193) fit4 <- lm(y ~ 0 + x1 + offset(intercept), dat) compare_lm(fit4, fit3) # Two predictors. fit5 <- lm(y ~ x1 + x2, dat) compare_lm(fit2, fit5) compare_lm(fit3, fit5) # Fix slope of x2 to 0.05 using offset(). fit6 <- lm(y ~ x1 + offset(0.05*x2), dat) compare_lm(fit6, fit5)x1 <- rnorm(193) x2 <- rnorm(193) y <- 0.3 + 0.2*x1 + 0.1*x2 + rnorm(193) dat <- data.frame(y, x1, x2) # Fix intercept to constant 1 using I(). fit1 <- lm(I(y - 1) ~ 0, dat) # Free intercept. fit2 <- lm(y ~ 1, dat) compare_lm(fit1, fit2) # One predictor. fit3 <- lm(y ~ x1, dat) compare_lm(fit2, fit3) # Fix intercept to 0.3 using offset(). intercept <- rep(0.3, 193) fit4 <- lm(y ~ 0 + x1 + offset(intercept), dat) compare_lm(fit4, fit3) # Two predictors. fit5 <- lm(y ~ x1 + x2, dat) compare_lm(fit2, fit5) compare_lm(fit3, fit5) # Fix slope of x2 to 0.05 using offset(). fit6 <- lm(y ~ x1 + offset(0.05*x2), dat) compare_lm(fit6, fit5)
Cut-off values of r given the sample size n.
cut_r(n)cut_r(n)
n |
Sample size of the r. |
Given n and p, t and then r could be determined. The formula used could be found in test_r()'s documentation.
A data.frame including the cut-off values of r at the significance levels of p = 0.1, 0.05, 0.01, 0.001. r with the absolute value larger than the cut-off value is significant at the corresponding significance level.
cut_r(193)cut_r(193)
A subset of data from a research about depression and coping.
depressdepress
depressA data frame with 94 rows and 237 columns:
Participant id
Class
Grade
Elite classes
0 = Control group, 1 = Intervention group
0 = girl, 1 = boy
Age in year
Cope scale, Time1, Item1, Problem-focused coping, 1 = very seldom, 5 = very often
Cope scale, Time1, Item3, Avoidance coping
cope scale, Time1, Item5, Emotion-focused coping
Cope scale, Time2, Item1, Problem-focused coping
Depression scale, Time1, Item1, 1 = very seldom, 5 = always
ECR-RS scale, Item1, attachment avoidance, 1 = very disagree, 7 = very agree
ECR-RS scale, Item2, attachment anxiety
Depression, Mean, Time1
Problem-focused coping, Mean, Time1
Emotion-focused coping, Mean, Time1
Avoidance coping, Mean, Time1
Attachment avoidance, Mean
Attachment anxiety, Mean
Keng package.
Compute the post-hoc power and/or plan the sample size for one or a set of predictors in linear regression
power_lm(PRE = 0.02, PC = 0, PA = 1, power = 0.8, sig.level = 0.05, n = NULL)power_lm(PRE = 0.02, PC = 0, PA = 1, power = 0.8, sig.level = 0.05, n = NULL)
PRE |
Proportional Reduction in Error. PRE = The square of partial correlation. Cohen (1988) suggested >=0.02, >=0.13, and >=0.26 as cut-off values of PRE for small, medium, and large effect sizes, respectively. |
PC |
Number of parameters of model C (compact model) without focal predictors of interest. |
PA |
Number of parameters of model A (augmented model) with focal predictors of interest. |
power |
Expected statistical power for effects of focal predictors. |
sig.level |
Expected significance level for effects of focal predictors. |
n |
The current sample size. If n is given, the post-hoc power would be computed. |
A list with 4 items: (1) post, the post-hoc F-test, lambda (non-centrality parameter),
and power for sample size n;
(2)minimum, the minimum sample size required for focal predictors to reach the
expected statistical power and significance level;
(3) prior, a data.frame including n_i, PC, PA,df_A_i, F_i, p_i, lambda_i, power_i.
_i indicates these statistics are the intermediate iterative results.
Each row of prior presents results for one possible sample size n_i.
Given n_i, df_A_i, F_i, p_i, lambda_i and power_i would be computed accordingly.
(4) A plot of power against sample size n.
The cut-off value of n for expected statistical power power and
expected significance level sig.level is annotated on the plot.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
power_lm()power_lm()
Scale a vector
Scale(x, m = NULL, sd = NULL, oadvances = NULL)Scale(x, m = NULL, sd = NULL, oadvances = NULL)
x |
The original vector. |
m |
The expected Mean of the scaled vector. |
sd |
The expected Standard Deviation (unit) of the scaled vector. |
oadvances |
The distance the Origin of x advances by. |
To scale x, its origin, or unit (sd), or both, could be changed.
If m = 0 or NULL, and sd = NULL, x would be mean-centered.
If m is a non-zero number, and sd = NULL, the mean of x would be transformed to m.
If m = 0 or NULL, and sd = 1, x would be standardized to be its z-score with m = 0 and m = 1.
The standardized score is not necessarily the z-score. If neither m nor sd is NULL,
x would be standardized to be a vector whose mean and standard deviation would be m and sd, respectively.
To standardize x, the mean and standard deviation of x are needed and computed,
for which the missing values of x are removed if any.
If oadvances is not NULL, the origin of x will advance with the standard deviation being unchanged.
In this case, Scale() could be used to pick points in simple slope analysis for moderation models.
Note that when oadvances is not NULL, m and sd must be NULL.
The scaled vector.
(x <- rnorm(10, 5, 2)) # Mean-center x. Scale(x) # Transform the mean of x to 3. Scale(x, m = 3) # Transform x to its z-score. Scale(x, sd = 1) # Standardize x with m = 100 and sd = 15. Scale(x, m = 100, sd = 15) # The origin of x advances by 3. Scale(x, oadvances = 3)(x <- rnorm(10, 5, 2)) # Mean-center x. Scale(x) # Transform the mean of x to 3. Scale(x, m = 3) # Transform x to its z-score. Scale(x, sd = 1) # Standardize x with m = 100 and sd = 15. Scale(x, m = 100, sd = 15) # The origin of x advances by 3. Scale(x, oadvances = 3)
Test r using the t-test and Fisher's z given r and n.
test_r(r, n)test_r(r, n)
r |
Pearson's correlation. |
n |
Sample size of r. |
To test the significance of the r using one-sample t-test,
the SE of the r is determined by the following formula: SE = sqrt((1 - r^2)/(n - 2)).
Another way is transforming r to Fisher's z using the following formula:
fz = atanh(r) with the SE of fz being sqrt(n - 3).
Note that Fisher's z is commonly used to compare two Pearson's correlations from independent samples.
Fisher's transformation is presented here only for satisfying the curiosity of users interested in the difference of t -test and Fisher's transformation.
A list including r, t -test of r (SE_r, t, p_r),
95% CI of r based on t -test (LLCI_r_t, ULCI_r_t),
fz (Fisher's z) of r, z -test of Fisher's z (SE_fz, z, p_fz), and 95% CI of r derived from fz.
Note that the returned CI of r may be out of r's valid range [-1, 1].
This "error" is deliberately left to users, who should correct the CI manually when reporting.
test_r(0.2, 193) # compare the p-values of t-test and Fisher's transformation for (i in seq(30, 200, 10)) { cat(c( "n =", i, ",", format( abs(test_r(0.2, i)[[1]][4] - test_r(0.2, i)[[2]][4]), nsmall = 12, scientific = FALSE)), fill = TRUE) }test_r(0.2, 193) # compare the p-values of t-test and Fisher's transformation for (i in seq(30, 200, 10)) { cat(c( "n =", i, ",", format( abs(test_r(0.2, i)[[1]][4] - test_r(0.2, i)[[2]][4]), nsmall = 12, scientific = FALSE)), fill = TRUE) }