Confidence Intervals for a 'std_selected' Class Object
Source:R/confint_stdmod.R
confint.std_selected.RdReturn the confidence intervals of estimates
in the output of std_selected() or std_selected_boot().
Usage
# S3 method for std_selected
confint(object, parm, level = 0.95, type, ...)Arguments
- object
The output of
std_selected()orstd_selected_boot().- parm
The parameters (coefficients) for which confidence intervals should be returned. If missing, the confidence intervals of all parameters will be returned.
- level
The level of confidence. For the confidence intervals returned by
lm(), default is .95, i.e., 95%. For the bootstrap percentile confidence intervals, default is the level used in callingstd_selected_boot(). If a level different from that in the original call is specified,full_outputneeds to be set in the call tostd_selected_boot()such that the original bootstrapping output is stored.- type
The type of the confidence intervals. If est to
"lm", returns the confidence interval given by theconfint()method oflm(). If set to"boot", the bootstrap percentile confidence intervals are returned. Default is"boot"if bootstrap estimates are stored inobject, and"lm"if bootstrap estimates are not stored.- ...
Arguments to be passed to
summary.lm().
Details
If bootstrapping is used to form the confidence interval by
std_selected_boot(),
users can request the percentile confidence intervals of
the bootstrap estimates. This method does not do the bootstrapping itself.
Author
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
Examples
# Load a sample data set
dat <- test_x_1_w_1_v_1_cat1_n_500
# Do a moderated regression by lm
lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat)
summary(lm_raw)
#>
#> Call:
#> lm(formula = dv ~ iv * mod + v1 + cat1, data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -2146.0 -431.9 -25.0 411.2 2309.3
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 308.767 4075.066 0.076 0.9396
#> iv 52.760 271.242 0.195 0.8459
#> mod 5.127 40.772 0.126 0.9000
#> v1 -12.760 10.174 -1.254 0.2104
#> cat1gp2 -158.673 71.834 -2.209 0.0276 *
#> cat1gp3 -43.166 75.283 -0.573 0.5666
#> iv:mod 3.416 2.709 1.261 0.2080
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 665 on 493 degrees of freedom
#> Multiple R-squared: 0.6352, Adjusted R-squared: 0.6307
#> F-statistic: 143 on 6 and 493 DF, p-value: < 2.2e-16
#>
# Standardize all variables except for categorical variables.
# Interaction terms are formed after standardization.
lm_std <- std_selected(lm_raw, to_center = ~ .,
to_scale = ~ .)
# Alternative: use to_standardize as a shortcut
# lm_std <- std_selected(lm_raw, to_standardize = ~ .)
summary(lm_std)
#>
#> Call to std_selected():
#> std_selected(lm_out = lm_raw, to_scale = ~., to_center = ~.)
#>
#> Selected variable(s) are centered by mean and/or scaled by SD
#> - Variable(s) centered: dv iv mod v1 cat1
#> - Variable(s) scaled: dv iv mod v1 cat1
#>
#> centered_by scaled_by Note
#> dv 6565.02965 1094.244465 Standardized (mean = 0, SD = 1)
#> iv 15.01576 2.039154 Standardized (mean = 0, SD = 1)
#> mod 100.39502 5.040823 Standardized (mean = 0, SD = 1)
#> v1 10.13884 2.938932 Standardized (mean = 0, SD = 1)
#> cat1 NA NA Nonnumeric
#>
#> Note:
#> - Categorical variables will not be centered or scaled even if
#> requested.
#>
#> Call:
#> lm(formula = dv ~ iv * mod + v1 + cat1, data = dat_mod)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.96117 -0.39474 -0.02285 0.37579 2.11040
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.0646 0.0483 1.3385 0.18136
#> iv 0.7374 0.0274 26.9480 < 0.001 ***
#> mod 0.2599 0.0274 9.4962 < 0.001 ***
#> v1 -0.0343 0.0273 -1.2542 0.21037
#> cat1gp2 -0.1450 0.0656 -2.2089 0.02764 *
#> cat1gp3 -0.0394 0.0688 -0.5734 0.56664
#> iv:mod 0.0321 0.0255 1.2608 0.20799
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.6077 on 493 degrees of freedom
#>
#> R-squared : 0.6352
#> Adjusted R-squared : 0.6307
#> ANOVA test of R-squared : F(6, 493) = 143.047, p < 0.001
#>
#> = Test the highest order term =
#> The highest order term : iv:mod
#> R-squared increase adding this term: 0.0012
#> F test of R-squared increase : F(1, 493) = 1.5895, p = 0.208
#>
#> Note:
#> - Estimates and their statistics are based on the data after
#> mean-centering, scaling, or standardization.
#> - One or more variables are scaled by SD or standardized. OLS standard
#> errors and confidence intervals may be biased for their coefficients.
#> Please use `std_selected_boot()`.
#>
confint(lm_std)
#> 2.5 % 97.5 %
#> (Intercept) -0.03021975 0.15938347
#> iv 0.68362100 0.79114661
#> mod 0.20612513 0.31367234
#> v1 -0.08795872 0.01941694
#> cat1gp2 -0.27398880 -0.01602419
#> cat1gp3 -0.17462329 0.09572673
#> iv:mod -0.01791790 0.08209267
# Use to_standardize as a shortcut
lm_std2 <- std_selected(lm_raw, to_standardize = ~ .)
# The results are the same
confint(lm_std)
#> 2.5 % 97.5 %
#> (Intercept) -0.03021975 0.15938347
#> iv 0.68362100 0.79114661
#> mod 0.20612513 0.31367234
#> v1 -0.08795872 0.01941694
#> cat1gp2 -0.27398880 -0.01602419
#> cat1gp3 -0.17462329 0.09572673
#> iv:mod -0.01791790 0.08209267
confint(lm_std2)
#> 2.5 % 97.5 %
#> (Intercept) -0.03021975 0.15938347
#> iv 0.68362100 0.79114661
#> mod 0.20612513 0.31367234
#> v1 -0.08795872 0.01941694
#> cat1gp2 -0.27398880 -0.01602419
#> cat1gp3 -0.17462329 0.09572673
#> iv:mod -0.01791790 0.08209267
all.equal(confint(lm_std), confint(lm_std2))
#> [1] TRUE
# With bootstrapping
# nboot = 100 just for illustration. nboot >= 2000 should be used in read
# research.
set.seed(89572)
lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ .,
to_center = ~ .,
nboot = 100)
summary(lm_std_boot)
#>
#> Call to std_selected_boot():
#> std_selected_boot(lm_out = lm_raw, to_scale = ~., to_center = ~.,
#> nboot = 100)
#>
#> Selected variable(s) are centered by mean and/or scaled by SD
#> - Variable(s) centered: dv iv mod v1 cat1
#> - Variable(s) scaled: dv iv mod v1 cat1
#>
#> centered_by scaled_by Note
#> dv 6565.02965 1094.244465 Standardized (mean = 0, SD = 1)
#> iv 15.01576 2.039154 Standardized (mean = 0, SD = 1)
#> mod 100.39502 5.040823 Standardized (mean = 0, SD = 1)
#> v1 10.13884 2.938932 Standardized (mean = 0, SD = 1)
#> cat1 NA NA Nonnumeric
#>
#> Note:
#> - Categorical variables will not be centered or scaled even if
#> requested.
#> - Nonparametric bootstrapping 95% confidence intervals computed.
#> - The number of bootstrap samples is 100.
#>
#> Call:
#> lm(formula = dv ~ iv * mod + v1 + cat1, data = dat_mod)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.96117 -0.39474 -0.02285 0.37579 2.11040
#>
#> Coefficients:
#> Estimate CI Lower CI Upper Std. Error t value Pr(>|t|)
#> (Intercept) 0.0646 -0.0194 0.1257 0.0483 1.3385 0.18136
#> iv 0.7374 0.6891 0.7934 0.0274 26.9480 < 0.001 ***
#> mod 0.2599 0.1974 0.3192 0.0274 9.4962 < 0.001 ***
#> v1 -0.0343 -0.0961 0.0171 0.0273 -1.2542 0.21037
#> cat1gp2 -0.1450 -0.2710 -0.0123 0.0656 -2.2089 0.02764 *
#> cat1gp3 -0.0394 -0.1477 0.0991 0.0688 -0.5734 0.56664
#> iv:mod 0.0321 -0.0049 0.0863 0.0255 1.2608 0.20799
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.6077 on 493 degrees of freedom
#>
#> R-squared : 0.6352
#> Adjusted R-squared : 0.6307
#> ANOVA test of R-squared : F(6, 493) = 143.047, p < 0.001
#>
#> = Test the highest order term =
#> The highest order term : iv:mod
#> R-squared increase adding this term: 0.0012
#> F test of R-squared increase : F(1, 493) = 1.5895, p = 0.208
#>
#> Note:
#> - Estimates and their statistics are based on the data after
#> mean-centering, scaling, or standardization.
#> - [CI Lower, CI Upper] are bootstrap percentile confidence intervals.
#> - Std. Error are not bootstrap SEs.
#>
# Bootstrap percentile intervals, default when bootstrap was conduced
confint(lm_std_boot)
#> 2.5 % 97.5 %
#> (Intercept) -0.019442340 0.12570734
#> iv 0.689068561 0.79335143
#> mod 0.197400624 0.31922399
#> v1 -0.096125083 0.01714287
#> cat1gp2 -0.270961023 -0.01233464
#> cat1gp3 -0.147733373 0.09914400
#> iv:mod -0.004904705 0.08631912
# Force OLS confidence intervals
confint(lm_std_boot, type = "lm")
#> 2.5 % 97.5 %
#> (Intercept) -0.03021975 0.15938347
#> iv 0.68362100 0.79114661
#> mod 0.20612513 0.31367234
#> v1 -0.08795872 0.01941694
#> cat1gp2 -0.27398880 -0.01602419
#> cat1gp3 -0.17462329 0.09572673
#> iv:mod -0.01791790 0.08209267
# Use to_standardize as a shortcut
set.seed(89572)
lm_std_boot2 <- std_selected_boot(lm_raw, to_standardize = ~ .,
nboot = 100)
# The results are the same
confint(lm_std_boot)
#> 2.5 % 97.5 %
#> (Intercept) -0.019442340 0.12570734
#> iv 0.689068561 0.79335143
#> mod 0.197400624 0.31922399
#> v1 -0.096125083 0.01714287
#> cat1gp2 -0.270961023 -0.01233464
#> cat1gp3 -0.147733373 0.09914400
#> iv:mod -0.004904705 0.08631912
confint(lm_std_boot2)
#> 2.5 % 97.5 %
#> (Intercept) -0.019442340 0.12570734
#> iv 0.689068561 0.79335143
#> mod 0.197400624 0.31922399
#> v1 -0.096125083 0.01714287
#> cat1gp2 -0.270961023 -0.01233464
#> cat1gp3 -0.147733373 0.09914400
#> iv:mod -0.004904705 0.08631912
all.equal(confint(lm_std_boot), confint(lm_std_boot2))
#> [1] TRUE