Pools univariate estimates of m repeated complete data analysis
Usage
pool.scalar(Q, U, n = Inf, k = 1, rule = c("rubin1987", "reiter2003"))
pool.scalar.syn(Q, U, n = Inf, k = 1, rule = "reiter2003")Arguments
- Q
A vector of univariate estimates of
mrepeated complete data analyses.- U
A vector containing the corresponding
mvariances of the univariate estimates.- n
A number providing the sample size. If nothing is specified, an infinite sample
n = Infis assumed.- k
A number indicating the number of parameters to be estimated. By default,
k = 1is assumed.- rule
A string indicating the pooling rule. Currently supported are
"rubin1987"(default, for missing data) and"reiter2003"(for synthetic data created from a complete data set).
Value
Returns a list with components.
m:Number of imputations.
qhat:The
munivariate estimates of repeated complete-data analyses.u:The corresponding
mvariances of the univariate estimates.qbar:The pooled univariate estimate, formula (3.1.2) Rubin (1987).
ubar:The mean of the variances (i.e. the pooled within-imputation variance), formula (3.1.3) Rubin (1987).
b:The between-imputation variance, formula (3.1.4) Rubin (1987).
t:The total variance of the pooled estimated, formula (3.1.5) Rubin (1987).
r:The relative increase in variance due to nonresponse, formula (3.1.7) Rubin (1987).
df:The degrees of freedom for t reference distribution by the method of Barnard-Rubin (1999).
fmi:The fraction missing information due to nonresponse, formula (3.1.10) Rubin (1987). (Not defined for synthetic data.)
Details
The function averages the univariate estimates of the complete data model, computes the total variance over the repeated analyses, and computes the relative increase in variance due to missing data or data synthesisation and the fraction of missing information.
References
Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons.
Reiter, J.P. (2003). Inference for Partially Synthetic, Public Use Microdata Sets. Survey Methodology, 29, 181-189.
Examples
# missing data imputation with with manual pooling
imp <- mice(nhanes, maxit = 2, m = 2, print = FALSE, seed = 18210)
fit <- with(data = imp, lm(bmi ~ age))
# manual pooling
summary(fit$analyses[[1]])
#>
#> Call:
#> lm(formula = bmi ~ age)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.1587 -3.0674 0.9413 2.3870 8.7413
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 28.1043 1.8853 14.91 2.61e-13 ***
#> age -1.5457 0.9723 -1.59 0.126
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 3.957 on 23 degrees of freedom
#> Multiple R-squared: 0.099, Adjusted R-squared: 0.05983
#> F-statistic: 2.527 on 1 and 23 DF, p-value: 0.1255
#>
summary(fit$analyses[[2]])
#>
#> Call:
#> lm(formula = bmi ~ age)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -7.3611 -3.6333 0.9389 2.3389 7.5389
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 29.189 2.019 14.460 4.92e-13 ***
#> age -1.428 1.041 -1.371 0.183
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 4.236 on 23 degrees of freedom
#> Multiple R-squared: 0.0756, Adjusted R-squared: 0.03541
#> F-statistic: 1.881 on 1 and 23 DF, p-value: 0.1835
#>
pool.scalar(Q = c(-1.5457, -1.428), U = c(0.9723^2, 1.041^2), n = 25, k = 2)
#> $m
#> [1] 2
#>
#> $qhat
#> [1] -1.5457 -1.4280
#>
#> $u
#> [1] 0.9453673 1.0836810
#>
#> $qbar
#> [1] -1.48685
#>
#> $ubar
#> [1] 1.014524
#>
#> $b
#> [1] 0.006926645
#>
#> $t
#> [1] 1.024914
#>
#> $df
#> [1] 20.97025
#>
#> $r
#> [1] 0.01024122
#>
#> $fmi
#> [1] 0.09272831
#>
# check: automatic pooling using broom
pool(fit)
#> Class: mipo m = 2
#> term m estimate ubar b t dfcom df
#> 1 (Intercept) 2 28.646618 3.814682 0.588114658 4.696854 23 10.72144
#> 2 age 2 -1.486715 1.014543 0.006947187 1.024964 23 20.96937
#> riv lambda fmi
#> 1 0.2312570 0.18782190 0.30620278
#> 2 0.0102714 0.01016697 0.09275848
# manual pooling for synthetic data created from complete data
imp <- mice(cars,
maxit = 2, m = 2, print = FALSE, seed = 18210,
where = matrix(TRUE, nrow(cars), ncol(cars))
)
fit <- with(data = imp, lm(speed ~ dist))
# manual pooling: extract Q and U
summary(fit$analyses[[1]])
#>
#> Call:
#> lm(formula = speed ~ dist)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.9740 -2.3144 -0.1494 3.1287 7.4115
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 10.15208 1.06236 9.556 1.10e-12 ***
#> dist 0.12182 0.02121 5.744 6.15e-07 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 3.618 on 48 degrees of freedom
#> Multiple R-squared: 0.4074, Adjusted R-squared: 0.395
#> F-statistic: 33 on 1 and 48 DF, p-value: 6.147e-07
#>
summary(fit$analyses[[2]])
#>
#> Call:
#> lm(formula = speed ~ dist)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -7.5830 -3.1680 -0.3479 3.3928 8.1902
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.46952 1.31136 7.221 3.37e-09 ***
#> dist 0.13209 0.02516 5.250 3.43e-06 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 4.271 on 48 degrees of freedom
#> Multiple R-squared: 0.3647, Adjusted R-squared: 0.3515
#> F-statistic: 27.56 on 1 and 48 DF, p-value: 3.428e-06
#>
pool.scalar.syn(Q = c(0.12182, 0.13209), U = c(0.02121^2, 0.02516^2), n = 50, k = 2)
#> $m
#> [1] 2
#>
#> $qhat
#> [1] 0.12182 0.13209
#>
#> $u
#> [1] 0.0004498641 0.0006330256
#>
#> $qbar
#> [1] 0.126955
#>
#> $ubar
#> [1] 0.0005414448
#>
#> $b
#> [1] 5.273645e-05
#>
#> $t
#> [1] 0.0005678131
#>
#> $df
#> [1] 463.7127
#>
#> $r
#> [1] 0.1460992
#>
#> $fmi
#> [1] NA
#>
# check: automatic pooling using broom
pool.syn(fit)
#> Class: mipo m = 2
#> term m estimate ubar b t dfcom df
#> 1 (Intercept) 2 9.8108000 1.4241330840 2.329428e-01 1.5406044600 48 174.9621
#> 2 dist 2 0.1269552 0.0005414288 5.273011e-05 0.0005677938 48 463.7928
#> riv lambda fmi
#> 1 0.2453522 NA NA
#> 2 0.1460860 NA NA