configural: An R package for profile analysis

Description

Overview of the configural package.

Details

The configural package provides tools for conducting configural and profile analyses. It currently supports criterion profile analysis (Davison & Davenport, 2002) and meta-analytic criterion profile analysis (Wiernik et al., 2019). Functions are provided to calculate criterion patterns and CPA variance decomposition, as well as for computing confidence intervals, shrinkage corrections, and fungible patterns.

Author(s)

Maintainer: Brenton M. Wiernik brenton@wiernik.org

See Also

Useful links:

• Report bugs at https://github.com/bwiernik/configural/issues

Quadratic form matrix product

Description

Calculate the quadratic form

Q=x^{\prime}Ax

Usage

A %&% x

Arguments

Value

The quadratic product

Examples

diag(5) %&% 1:5

Locate extrema of fungible OLS regression weights

Description

Locate extrema of fungible OLS regression weights

Usage

.fungible_extrema(
  theta,
  Rxx,
  rxy,
  Nstarts = 1000,
  MaxMin = c("min", "max"),
  silent = FALSE
)

Arguments

Value

A list containing the alternative weights and other fungible weights estimation parameters

Author(s)

Adapted from fungible::fungibleExtrema() by Niels Waller and Jeff Jones

Adjust a regression model R-squared for overfitting

Description

Estimate shrinkage for regression models

Usage

adjust_Rsq(Rsq, n, p, adjust = c("fisher", "pop", "cv"))

Arguments

Value

An adjusted R-squared value.

References

Shieh, G. (2008). Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient. Organizational Research Methods, 11(2), 387–407. doi:10.1177/1094428106292901

Examples

adjust_Rsq(.55, 100, 6, adjust = "pop")

Make a matrix symmetric by averaging with its transpose

Description

Makes a matrix symmetric by averaging the elements of the matrix and its transpose. When This function fills in NA elements of a matrix with the corresponding value from the matrix transpose, if available

Usage

complete_matrix(m, na.rm = TRUE)

Arguments

Value

A completed matrix.

Examples

predictors <- c('auto', 'skill_var', 'task_var', 'task_sig', 'task_id',
'fb_job', 'job_comp', 'interdep', 'fb_others', 'soc_support')
m <- jobchar$sevar_r[c('perform', predictors), c('perform', predictors)]
complete_matrix(m)

Calculate the asymptotic sampling covariance matrix for the unique elements of a correlation matrix

Description

Calculate the asymptotic sampling covariance matrix for the unique elements of a correlation matrix

Usage

cor_covariance(r, n)

Arguments

Value

The asymptotic sampling covariance matrix

Author(s)

Based on an internal function from the fungible package by Niels Waller

References

Nel, D. G. (1985). A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients. Linear Algebra and Its Applications, 67, 137–145. doi:10.1016/0024-3795(85)90191-0

Examples

cor_covariance(matrix(c(1, .2, .3, .2, 1, .3, .3, .3, 1), ncol = 3), 100)

Estimate the asymptotic sampling covariance matrix for the unique elements of a meta-analytic correlation matrix

Description

Estimate the asymptotic sampling covariance matrix for the unique elements of a meta-analytic correlation matrix

Usage

cor_covariance_meta(
  r,
  n,
  sevar,
  source = NULL,
  rho = NULL,
  sevar_rho = NULL,
  n_overlap = NULL
)

Arguments

Details

If both source and n_overlap are NULL, it is assumed that all meta-analytic correlations come from the the same source.

Value

The estimated asymptotic sampling covariance matrix

References

Nel, D. G. (1985). A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients. Linear Algebra and Its Applications, 67, 137–145. doi:10.1016/0024-3795(85)90191-0

Wiernik, B. M. (2018). Accounting for dependency in meta-analytic structural equations modeling: A flexible alternative to generalized least squares and two-stage structural equations modeling. Unpublished manuscript.

Examples

cor_covariance_meta(r = mindfulness$r, n = mindfulness$n,
                    sevar = mindfulness$sevar_r, source = mindfulness$source)

Generate labels for correlations from a vector of variable names

Description

This function returns a vector of labels for the unique correlations between pairs of variables from a supplied vector of variable names

Usage

cor_labels(var_names)

Arguments

Value

A vector of correlation labels

Examples

cor_labels(colnames(mindfulness$r))

Conduct criterion profile analysis using a correlation matrix

Description

Conduct criterion profile analysis using a correlation matrix

Usage

cpa_mat(
  formula,
  cov_mat,
  n = NULL,
  se_var_mat = NULL,
  se_beta_method = c("normal", "lm"),
  adjust = c("fisher", "pop", "cv"),
  conf_level = 0.95,
  ...
)

Arguments

Value

An object of class "cpa" containing the criterion pattern vector and CPA variance decomposition

References

Jones, J. A., & Waller, N. G. (2015). The normal-theory and asymptotic distribution-free (ADF) covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior. Psychometrika, 80(2), 365–378. doi:10.1007/s11336-013-9380-y

Revelle, W., Condon, D. M., Wilt, J., French, J. A., Brown, A., & Elleman, L. G. (2017). Web- and phone-based data collection using planned missing designs. In N. G. Fielding, R. M. Lee, & G. Blank, The SAGE Handbook of Online Research Methods (pp. 578–594). SAGE Publications. doi:10.4135/9781473957992.n33

Wiernik, B. M., Wilmot, M. P., Davison, M. L., & Ones, D. S. (2019). Meta-analytic criterion profile analysis. Psychological Methods doi:10.1037/met0000305

Examples

sevar <- cor_covariance_meta(mindfulness$r, mindfulness$n, mindfulness$sevar_r, mindfulness$source)
cpa_mat(mindfulness ~ ES + A + C + Ex + O,
          cov_mat = mindfulness$r,
          n = NULL,
          se_var_mat = sevar,
          adjust = "pop")

Compute CPA level and pattern scores for a set of data

Description

Compute CPA level and pattern scores for a set of data

Usage

cpa_scores(
  cpa_mod,
  newdata = NULL,
  augment = TRUE,
  cpa_names = c("cpa_lev", "cpa_pat"),
  scale = FALSE,
  scale_center = TRUE,
  scale_scale = TRUE
)

Arguments

Value

A data frame containing the CPA score variables.

Examples

sevar <- cor_covariance_meta(mindfulness$r, mindfulness$n, mindfulness$sevar_r, mindfulness$source)
cpa_mod <- cpa_mat(mindfulness ~ ES + A + C + Ex + O,
                   cov_mat = mindfulness$r,
                   n = NULL,
                   se_var_mat = sevar,
                   adjust = "pop")

newdata <- data.frame(ES = c(4.2, 3.2, 3.4, 4.2, 3.8, 4.0, 5.6, 2.8, 3.4, 2.8),
                      A  = c(4.0, 4.2, 3.8, 4.6, 4.0, 4.6, 4.6, 2.6, 3.6, 5.4),
                      C  = c(2.8, 4.0, 4.0, 3.0, 4.4, 5.6, 4.4, 3.4, 4.0, 5.6),
                      Ex = c(3.8, 5.0, 4.2, 3.6, 4.8, 5.6, 4.2, 2.4, 3.4, 4.8),
                      O  = c(3.0, 4.0, 4.8, 3.2, 3.6, 5.0, 5.4, 4.2, 5.0, 5.2)
                      )

newdata_cpa <- cpa_scores(cpa_mod, newdata, augment = FALSE)
newdata_augment <- cpa_scores(cpa_mod, newdata, augment = TRUE)

Meta-analytic correlations among Big Five personality traits and psychological disorders

Description

Big Five intercorrelations from Davies et al. (2015). Big Five–psychological disorder correlations from Kotov et al. (2010). Note that there were several duplicate or missing values in the reported data table in the published article. These results are based on corrected data values.

Usage

data(disorders)

Format

list with entries r (mean observed correlations), rho (mean corrected correlations), n (sample sizes), sevar_r (sampling error variances for mean observed correlations), sevar_rho (sampling error variances for mean corrected correlations), and source (character labels indicating which meta-analytic correlations came from the same source)

References

Davies, S. E., Connelly, B. L., Ones, D. S., & Birkland, A. S. (2015). The general factor of personality: The “Big One,” a self-evaluative trait, or a methodological gnat that won’t go away? Personality and Individual Differences, 81, 13–22. doi:10.1016/j.paid.2015.01.006

Kotov, R., Gamez, W., Schmidt, F., & Watson, D. (2010). Linking “big” personality traits to anxiety, depressive, and substance use disorders: A meta-analysis. Psychological Bulletin, 136(5), 768–821. doi:10.1037/a0020327

Examples

data(disorders)

Locate extrema of fungible weights for regression and related models

Description

Generates fungible regression weights (Waller, 2008) and related results using the method by Waller and Jones (2010).

Usage

fungible(
  object,
  theta = 0.005,
  Nstarts = 1000,
  MaxMin = c("min", "max"),
  silent = FALSE,
  ...
)

Arguments

Value

A list containing the alternative weights and other fungible weights estimation parameters

Author(s)

Niels Waller, Jeff Jones, Brenton M. Wiernik. Adapted from fungible::fungibleExtrema().

References

Waller, N. G. (2008). Fungible weights in multiple regression. Psychometrika, 73(4), 691–703. doi:10.1007/s11336-008-9066-z

Waller, N. G., & Jones, J. A. (2009). Locating the extrema of fungible regression weights. Psychometrika, 74(4), 589–602. doi:10.1007/s11336-008-9087-7

Examples

mind <- cpa_mat(mindfulness ~ ES + A + C + Ex + O,
                cov_mat = mindfulness$r,
                n = harmonic_mean(vechs(mindfulness$n)),
                se_var_mat = cor_covariance_meta(mindfulness$r,
                                                 mindfulness$n,
                                                 mindfulness$sevar_r,
                                                 mindfulness$source),
                adjust = "pop")
mind_fung <- fungible(mind, Nstarts = 100)

Locate extrema of fungible criterion profile patterns

Description

Identify maximally similar or dissimilar criterion patterns in criterion profile analysis

Usage

## S3 method for class 'cpa'
fungible(
  object,
  theta = 0.005,
  Nstarts = 1000,
  MaxMin = c("min", "max"),
  silent = FALSE,
  ...
)

Arguments

Value

A list containing the alternative weights and other fungible weights estimation parameters

References

Wiernik, B. M., Wilmot, M. P., Davison, M. L., & Ones, D. S. (2020). Meta-analytic criterion profile analysis. Psychological Methods. doi:10.1037/met0000305

Examples

mind <- cpa_mat(mindfulness ~ ES + A + C + Ex + O,
                cov_mat = mindfulness$r,
                n = harmonic_mean(vechs(mindfulness$n)),
                se_var_mat = cor_covariance_meta(mindfulness$r,
                                                 mindfulness$n,
                                                 mindfulness$sevar_r,
                                                 mindfulness$source),
                adjust = "pop")
mind_fung <- fungible(mind, Nstarts = 100)

Locate extrema of fungible OLS regression weights

Description

Identify maximally similar or dissimilar sets of fungible standardized regression coefficients from an OLS regression model

Usage

## S3 method for class 'lm'
fungible(
  object,
  theta = 0.005,
  Nstarts = 1000,
  MaxMin = c("min", "max"),
  silent = FALSE,
  ...
)

Arguments

Value

A list containing the alternative weights and other fungible weights estimation parameters

References

Waller, N. G., & Jones, J. A. (2009). Locating the extrema of fungible regression weights. Psychometrika, 74(4), 589–602. doi:10.1007/s11336-008-9087-7

Examples

lm_mtcars <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb,
                data = mtcars)
lm_mtcars_fung <- fungible(lm_mtcars, Nstarts = 100)

Meta-analytic correlations of Graduate Record Examination subtests with graduate grade point average

Description

Correlations between GRE subtests and graduate student GPA from Kuncel et al. (2001).

Usage

data(gre)

Format

list with entries r (mean observed correlations), rho (mean corrected correlations), n (sample sizes), sevar_r (sampling error variances for mean observed correlations), sevar_rho (sampling error variances for mean corrected correlations), and source (character labels indicating which meta-analytic correlations came from the same source)

Details

GRE–GPA correlations in rho are corrected for direct range restriction on the GRE and unreliability in GPA. Subtest intercorrelations in rho are observed correlations computed among applicant norm samples. These values are also used in r. Due to compensatory selection on GRE scores, these values will not accurately reflect subtest intercorrelations in selected-student (range-restricted) samples. sevar_rho andsevar_r for GRE subtest intercorrelations are computed with an assumed SD_ρ = .02.

References

Kuncel, N. R., Hezlett, S. A., & Ones, D. S. (2001). A comprehensive meta-analysis of the predictive validity of the graduate record examinations: Implications for graduate student selection and performance. Psychological Bulletin, 127(1), 162–181. doi:10.1037/0033-2909.127.1.162

Examples

data(gre)

Find the harmonic mean of a vector, matrix, or columns of a data.frame

Description

The harmonic mean is merely the reciprocal of the arithmetic mean of the reciprocals.

Usage

harmonic_mean(x, na.rm = TRUE, zero = TRUE)

Arguments

Value

The harmonic mean of x

Author(s)

Adapted from psych::harmonic.mean() by William Revelle

Examples

harmonic_mean(1:10)

Meta-analytic correlations of HRM practices with organizational financial performance

Description

Human resource management practice–organizational financial performance correlations from Combs et al. (2006). Intercorrelations among HRM practices from Guest et al. (2004).

Usage

data(hrm)

Format

list with entries r (mean observed correlations), rho (mean corrected correlations), n (sample sizes), sevar_r (sampling error variances for mean observed correlations), sevar_rho (sampling error variances for mean corrected correlations), and source (character labels indicating which meta-analytic correlations came from the same source)

References

Combs, J., Liu, Y., Hall, A., & Ketchen, D. (2006). How much do high-performance work practices matter? A meta-analysis of their effects on organizational performance. Personnel Psychology, 59(3), 501–528. doi:10.1111/j.1744-6570.2006.00045.x

Guest, D., Conway, N., & Dewe, P. (2004). Using sequential tree analysis to search for ‘bundles’ of HR practices. Human Resource Management Journal, 14(1), 79–96. doi:10.1111/j.1748-8583.2004.tb00113.x

Examples

data(hrm)

Meta-analytic correlations of job characteristics with performance and satisfaction

Description

Self-rated job characteristics intercorrelations and correlations with other-rated job performance and self-rated job satisfaction from Humphrey et al. (2007).

Usage

data(jobchar)

Format

list with entries r (mean observed correlations), rho (mean corrected correlations), n (sample sizes), sevar_r (sampling error variances for mean observed correlations), sevar_rho (sampling error variances for mean corrected correlations), and source (character labels indicating which meta-analytic correlations came from the same source)

References

Humphrey, S. E., Nahrgang, J. D., & Morgeson, F. P. (2007). Integrating motivational, social, and contextual work design features: A meta-analytic summary and theoretical extension of the work design literature. Journal of Applied Psychology, 92(5), 1332–1356. doi:10.1037/0021-9010.92.5.1332

Examples

data(jobchar)
predictors <- c('auto', 'skill_var', 'task_var', 'task_sig', 'task_id',
                'fb_job', 'job_comp', 'interdep', 'fb_others', 'soc_support')
sevar_jobchar_perf <-
  cor_covariance_meta(
    r = jobchar$r[c('perform', predictors), c('perform', predictors)],
                    n = jobchar$n[c('perform', predictors), c('perform', predictors)],
                    sevar = jobchar$sevar_r[c('perform', predictors), c('perform', predictors)],
                    rho = jobchar$rho[c('perform', predictors), c('perform', predictors)],
                    sevar_rho = jobchar$sevar_rho[c('perform', predictors),
                                                  c('perform', predictors)],
                    source = jobchar$source[c('perform', predictors), c('perform', predictors)])
cpa_jobchar_perf <- cpa_mat(perform ~ auto + skill_var + task_var + task_sig +
                              task_id + fb_job + job_comp +
                              interdep + fb_others + soc_support,
                            cov_mat = jobchar$rho,
                            n = harmonic_mean(as.vector(jobchar$n[c('perform', predictors),
                                                                  c('perform', predictors)])),
                            se_var_mat = sevar_jobchar_perf,
                            adjust = "pop", conf_level = .95)

Meta-analytic correlations among Big Five personality traits and trait mindfulness

Description

Big Five intercorrelations from Davies et al. (2015). Big Five–Mindfulness correlations from Hanley and Garland (2017). Coefficient alpha for mindfulness measures taken from Giluk (2009).

Usage

data(mindfulness)

Format

list with entries r (mean observed correlations), rho (mean corrected correlations), n (sample sizes), sevar_r (sampling error variances for mean observed correlations), sevar_rho (sampling error variances for mean corrected correlations), and source (character labels indicating which meta-analytic correlations came from the same source)

References

Davies, S. E., Connelly, B. L., Ones, D. S., & Birkland, A. S. (2015). The general factor of personality: The “Big One,” a self-evaluative trait, or a methodological gnat that won’t go away? Personality and Individual Differences, 81, 13–22. doi:10.1016/j.paid.2015.01.006

Giluk, T. L. (2009). Mindfulness, Big Five personality, and affect: A meta-analysis. Personality and Individual Differences, 47(8), 805–811. doi:10.1016/j.paid.2009.06.026

Hanley, A. W., & Garland, E. L. (2017). The mindful personality: A meta-analysis from a cybernetic perspective. Mindfulness, 8(6), 1456–1470. doi:10.1007/s12671-017-0736-8

Examples

data(mindfulness)

Effective sample size

Description

Estimate an effective sample size for a statistic given the observed statistic and the estimated sampling error variance (cf. Revelle et al., 2017).

Usage

n_effective_R2(R2, var_R2, p)

Arguments

Details

n_effective_R2 estimates the effective sample size for the R^2^ value from an OLS regression model, using the sampling error variance formula from Cohen et al. (2003).

Value

An effective sample size.

References

Revelle, W., Condon, D. M., Wilt, J., French, J. A., Brown, A., & Elleman, L. G. (2017). Web- and phone-based data collection using planned missing designs. In N. G. Fielding, R. M. Lee, & G. Blank, The SAGE Handbook of Online Research Methods (pp. 578–594). SAGE Publications. doi:10.4135/9781473957992.n33

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Routledge. doi:10.4324/9780203774441

Examples

n_effective_R2(0.3953882, 0.0005397923, 5)

Correlations between study design moderators and effect sizes for prejudice reduction following intergroup contact

Description

Correlations among study design moderators and study design moderator–observed prejudice reduction effect sizes from Pettigrew and Tropp (2008). Note that correlations with effect size have been reverse-coded so that a positive correlation indicates that a higher level of the moderator is associated with larger prejudice reduction.

Usage

data(prejudice)

Format

list with entries r (observed correlations among moderators) and k (number of samples in meta-analysis)

References

Pettigrew, T. F., & Tropp, L. R. (2006). A meta-analytic test of intergroup contact theory. Journal of Personality and Social Psychology, 90(5), 751–783. doi:10.1037/0022-3514.90.5.751

Examples

data(prejudice)

Meta-analytic correlations among team processes and team effectiveness

Description

Team process intercorrelations and team process–team performance/affect correlations from LePine et al. (2008).

Usage

data(team)

Format

list with entries r (mean observed correlations), rho (mean corrected correlations), n (sample sizes), sevar_r (sampling error variances for mean observed correlations), sevar_rho (sampling error variances for mean corrected correlations), and source (character labels indicating which meta-analytic correlations came from the same source)

Details

Note that LePine et al. (2008) did not report confidence intervals, sampling error variances, or heterogeneity estimates for correlations among team processes; included sampling error variances in this list are based on total sample size only and do not include uncertainty stemming from any effect size heterogeneity.

References

LePine, J. A., Piccolo, R. F., Jackson, C. L., Mathieu, J. E., & Saul, J. R. (2008). A meta-analysis of teamwork processes: tests of a multidimensional model and relationships with team effectiveness criteria. Personnel Psychology, 61(2), 273–307. doi:10.1111/j.1744-6570.2008.00114.x

Examples

data(team)

Calculate a transition matrix for a symmetric matrix

Description

The transition matrix extracts the lower triangular elements from a vectorized symmetric matrix (Nel, 1985).

Usage

transition(p)

Arguments

Author(s)

Based on internal functions from the fungible package by Niels Waller

References

Nel, D. G. (1985). A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients. Linear Algebra and Its Applications, 67, 137–145. doi:10.1016/0024-3795(85)90191-0

Examples

transition(5)

Estimate the sampling error variance for criterion profile analysis parameters

Description

Estimate the sampling error variance for criterion profile analysis parameters

Usage

var_error_cpa(
  Rxx,
  rxy,
  n = NULL,
  se_var_mat = NULL,
  adjust = c("fisher", "pop", "cv")
)

Arguments

Value

A list containing sampling covariance matrices or sampling error variance estimates for CPA parameters

Examples

var_error_cpa(mindfulness$rho[1:5, 1:5], mindfulness$rho[1:5, 6], n = 17060)

Vectorize a matrix

Description

cvec returns the column-wise vectorization of an input matrix (stacking the columns on one another). rvec returns the row-wise vectorization of an input matrix (concatenating the rows after each other). vech returns the column-wise half-vectorization of an input matrix (stacking the lower triangular elements of the matrix, including the diagonal). vechs returns the strict column-wise half-vectorization of an input matrix (stacking the lower triangular elements of the matrix, excluding the diagonal). All functions return the output as a vector.

Usage

vech(x)

vechs(x)

cvec(x)

rvec(x)

Arguments

Value

A vector of values

Author(s)

Based on functions from the the OpenMx package

Examples

cvec(matrix(1:9, 3, 3))
rvec(matrix(1:9, 3, 3))
vech(matrix(1:9, 3, 3))
vechs(matrix(1:9, 3, 3))
vechs(matrix(1:12, 3, 4))

Inverse vectorize a matrix

Description

These functions return the symmetric matrix that produces the given half-vectorization result.

Usage

vech2full(x)

vechs2full(x, diagonal = 1)

Arguments

Details

The input consists of a vector of the elements in the lower triangle of the resulting matrix (for vech2full, including the elements along the diagonal of the matrix, as a column vector), filled column-wise. For vechs2full, the diagonal values are filled as 1 by default, alternative values can be specified using the diag argument. The inverse half-vectorization takes a vector and reconstructs a symmetric matrix such that vech2full(vech(x)) is identical to x if x is symmetric.

Value

A symmetric matrix

Author(s)

Based on functions from the the OpenMx package

Examples

vech2full(c(1, 2, 3, 5, 6, 9))
vechs2full(c(2, 3, 6), diagonal = 0)

Compute weighted covariances

Description

Compute the weighted covariance among variables in a matrix or between the variables in two separate matrices/vectors.

Usage

wt_cov(
  x,
  y = NULL,
  wt = NULL,
  as_cor = FALSE,
  use = c("everything", "listwise", "pairwise"),
  unbiased = TRUE,
  df_type = c("count", "sum_wts")
)

wt_cor(x, y = NULL, wt = NULL, use = "everything")

Arguments

Value

Scalar, vector, or matrix of covariances.

Author(s)

Jeffrey A. Dahlke

Examples

wt_cov(x = c(1, 0, 2), y = c(1, 2, 3), wt = c(1, 2, 2), as_cor = FALSE, use = "everything")
wt_cov(x = c(1, 0, 2), y = c(1, 2, 3), wt = c(1, 2, 2), as_cor = TRUE, use = "everything")
wt_cov(x = cbind(c(1, 0, 2), c(1, 2, 3)), wt = c(1, 2, 2), as_cor = FALSE, use = "everything")
wt_cov(x = cbind(c(1, 0, 2), c(1, 2, 3)), wt = c(1, 2, 2), as_cor = TRUE, use = "everything")
wt_cov(x = cbind(c(1, 0, 2, NA), c(1, 2, 3, 3)),
       wt = c(1, 2, 2, 1), as_cor = FALSE, use = "listwise")
wt_cov(x = cbind(c(1, 0, 2, NA), c(1, 2, 3, 3)),
       wt = c(1, 2, 2, 1), as_cor = TRUE, use = "listwise")

Weighted descriptive statistics for a vector of numbers

Description

Compute the weighted mean and variance of a vector of numeric values. If no weights are supplied, defaults to computing the unweighted mean and the unweighted maximum-likelihood variance.

Usage

wt_dist(
  x,
  wt = rep(1, length(x)),
  unbiased = TRUE,
  df_type = c("count", "sum_wts")
)

wt_mean(x, wt = rep(1, length(x)))

wt_var(
  x,
  wt = rep(1, length(x)),
  unbiased = TRUE,
  df_type = c("count", "sum_wts")
)

Arguments

Details

The weighted mean is computed as

\bar{x}_{w}=\frac{\Sigma_{i=1}^{k}x_{i}w_{i}}{\Sigma_{i=1}^{k}w_{i}}

where x is a numeric vector and w is a vector of weights.

The weighted variance is computed as

var_{w}(x)=\frac{\Sigma_{i=1}^{k}\left(x_{i}-\bar{x}_{w}\right)^{2}w_{i}}{\Sigma_{i=1}^{k}w_{i}}

and the unbiased weighted variance is estimated by multiplying var_{w}(x) by \frac{k}{k-1}.

Value

A weighted mean and variance if weights are supplied or an unweighted mean and variance if weights are not supplied.

Author(s)

Jeffrey A. Dahlke

Examples

wt_dist(x = c(.1, .3, .5), wt = c(100, 200, 300))
wt_mean(x = c(.1, .3, .5), wt = c(100, 200, 300))
wt_var(x = c(.1, .3, .5), wt = c(100, 200, 300))