With the psfmi_lm function you can pool Linear
regression models by using
the following pooling methods: RR (Rubin’s Rules), D1, D2 and MPR
(Median R Rule).
You can also use forward or backward selection from the pooled model.
This vignette show you examples of how to apply these procedures.
library(psfmi)
pool_lm <- psfmi_lm(data=lbpmilr, nimp=5, impvar="Impnr",
formula = Pain ~ Gender + Smoking +
Function + JobControl + JobDemands + SocialSupport,
method="D1")
pool_lm$RR_model
#> $`Step 1 - no variables removed -`
#> term estimate std.error statistic df p.value
#> 1 (Intercept) 7.626750501 2.37470136 3.21166721 103.21605 0.001760151
#> 2 Gender -0.549897436 0.41763180 -1.31670395 97.10997 0.191036859
#> 3 Smoking -0.184822738 0.35459284 -0.52122524 60.23783 0.604120893
#> 4 Function -0.126983721 0.04264394 -2.97776686 46.48759 0.004600709
#> 5 JobControl -0.018201443 0.01884372 -0.96591573 117.54453 0.336069460
#> 6 JobDemands 0.015351105 0.03590006 0.42760673 121.85071 0.669692207
#> 7 SocialSupport -0.003435975 0.05621115 -0.06112622 96.21255 0.951385488Back to Examples
Pooling linear regression models over 5 imputed datasets with backward selection using a p-value of 0.05 and as method D1 and forcing the predictor "Smoking" in the models during backward selection.
library(psfmi)
pool_lm <- psfmi_lm(data=lbpmilr, nimp=5, impvar="Impnr",
formula = Pain ~ Gender + Smoking +
Function + JobControl + JobDemands + SocialSupport,
keep.predictors = "Smoking", method="D1", p.crit=0.05,
direction="BW")
#> Removed at Step 1 is - SocialSupport
#> Removed at Step 2 is - JobDemands
#> Removed at Step 3 is - JobControl
#> Removed at Step 4 is - Gender
#>
#> Selection correctly terminated,
#> No more variables removed from the model
pool_lm$RR_model_final
#> $`Step 5`
#> term estimate std.error statistic df p.value
#> 1 (Intercept) 6.7504947 0.47607990 14.1793314 78.48419 2.368256e-23
#> 2 Smoking -0.1998222 0.35556369 -0.5619871 57.20990 5.763201e-01
#> 3 Function -0.1403048 0.04077998 -3.4405314 51.97198 1.153144e-03
pool_lm$multiparm_final
#> $`Step 5`
#> p-values D1 F-statistic
#> Smoking 0.5753099186 0.3158295
#> Function 0.0008794238 11.8372561
pool_lm$predictors_out
#> Gender Smoking Function JobControl JobDemands SocialSupport
#> Step 1 0 0 0 0 0 1
#> Step 2 0 0 0 0 1 0
#> Step 3 0 0 0 1 0 0
#> Step 4 1 0 0 0 0 0
#> Removed 1 0 0 1 1 1Back to Examples
Pooling linear regression models over 5 imputed datasets with backward selection using a p-value of 0.05 and as method D1 and forcing the predictor "Smoking" in the models during backward selection.
library(psfmi)
pool_lm <- psfmi_lm(data=lbpmilr, nimp=5, impvar="Impnr",
formula = Pain ~ Gender + Smoking +
Function + JobControl + JobDemands + SocialSupport,
keep.predictors = "Smoking", method="MPR", p.crit=0.05,
direction="BW")
#> Removed at Step 1 is - SocialSupport
#> Removed at Step 2 is - JobDemands
#> Removed at Step 3 is - JobControl
#> Removed at Step 4 is - Gender
#>
#> Selection correctly terminated,
#> No more variables removed from the model
pool_lm$RR_model_final
#> $`Step 5`
#> term estimate std.error statistic df p.value
#> 1 (Intercept) 6.7504947 0.47607990 14.1793314 78.48419 2.368256e-23
#> 2 Smoking -0.1998222 0.35556369 -0.5619871 57.20990 5.763201e-01
#> 3 Function -0.1403048 0.04077998 -3.4405314 51.97198 1.153144e-03
pool_lm$multiparm_final
#> $`Step 5`
#> p-value MPR
#> Smoking 0.6019832504
#> Function 0.0001268997
pool_lm$predictors_out
#> Gender Smoking Function JobControl JobDemands SocialSupport
#> Step 1 0 0 0 0 0 1
#> Step 2 0 0 0 0 1 0
#> Step 3 0 0 0 1 0 0
#> Step 4 1 0 0 0 0 0
#> Removed 1 0 0 1 1 1Back to Examples
Pooling linear regression models over 5 imputed datasets with BS using a p-value of 0.05 and as method D2. Several interaction terms, including a categorical predictor, are part of the selection procedure.
library(psfmi)
pool_lm <- psfmi_lm(data=lbpmilr, nimp=5, impvar="Impnr",
formula = Pain ~ Gender + Smoking +
Function + JobControl + factor(Carrying) +
factor(Satisfaction) +
factor(Carrying):Smoking + Gender:Smoking,
method="D2", p.crit=0.05,
direction="BW")
#> Removed at Step 1 is - Function
#> Removed at Step 2 is - Gender*Smoking
#> Removed at Step 3 is - Smoking*factor(Carrying)
#> Removed at Step 4 is - Smoking
#> Removed at Step 5 is - JobControl
#> Removed at Step 6 is - Gender
#>
#> Selection correctly terminated,
#> No more variables removed from the model
pool_lm$RR_model_final
#> $`Step 7`
#> term estimate std.error statistic df p.value
#> 1 (Intercept) 3.8156476 0.3621860 10.5350490 129.49014 4.010553e-19
#> 2 factor(Carrying)2 0.8759161 0.3761904 2.3283850 113.24274 2.166656e-02
#> 3 factor(Carrying)3 1.8001704 0.3746799 4.8045553 145.87249 3.811778e-06
#> 4 factor(Satisfaction)2 0.1385358 0.3729809 0.3714288 108.41273 7.110431e-01
#> 5 factor(Satisfaction)3 1.4420012 0.4685986 3.0772635 74.55846 2.921715e-03
pool_lm$multiparm_final
#> $`Step 7`
#> p-values D2 F-statistic
#> factor(Carrying) 1.653888e-05 11.150999
#> factor(Satisfaction) 7.789587e-03 5.372204
pool_lm$predictors_out
#> Gender Smoking Function JobControl factor(Carrying)
#> Step 1 0 0 1 0 0
#> Step 2 0 0 0 0 0
#> Step 3 0 0 0 0 0
#> Step 4 0 1 0 0 0
#> Step 5 0 0 0 1 0
#> Step 6 1 0 0 0 0
#> Removed 1 1 1 1 0
#> factor(Satisfaction) Smoking*factor(Carrying) Gender*Smoking
#> Step 1 0 0 0
#> Step 2 0 0 1
#> Step 3 0 1 0
#> Step 4 0 0 0
#> Step 5 0 0 0
#> Step 6 0 0 0
#> Removed 0 1 1Back to Examples
Same as above but now forcing several predictors, including interaction terms, in the model during BS.
library(psfmi)
pool_lm <- psfmi_lm(data=lbpmilr, nimp=5, impvar="Impnr",
formula = Pain ~ Gender + Smoking +
Function + JobControl + factor(Carrying) + factor(Satisfaction) +
factor(Carrying):Smoking + Gender:Smoking,
keep.predictors = c("Smoking*Carrying", "JobControl"), method="D1",
p.crit=0.05, direction="BW")
#> Removed at Step 1 is - Function
#> Removed at Step 2 is - Gender*Smoking
#> Removed at Step 3 is - Gender
#>
#> Selection correctly terminated,
#> No more variables removed from the model
pool_lm$RR_model_final
#> $`Step 4`
#> term estimate std.error statistic df
#> 1 (Intercept) 5.05673749 1.11537162 4.5336796 87.35469
#> 2 Smoking -0.75879295 0.59455328 -1.2762405 50.60796
#> 3 JobControl -0.01558801 0.01737846 -0.8969733 87.93658
#> 4 factor(Carrying)2 0.51735642 0.51915658 0.9965325 132.99359
#> 5 factor(Carrying)3 1.31863192 0.50113424 2.6312948 126.77358
#> 6 factor(Satisfaction)2 0.11077123 0.37320587 0.2968100 117.98206
#> 7 factor(Satisfaction)3 1.44590689 0.48154484 3.0026423 64.65768
#> 8 Smoking:factor(Carrying)2 0.81312389 0.77812973 1.0449721 87.32029
#> 9 Smoking:factor(Carrying)3 1.13073244 0.79050622 1.4303903 104.46161
#> p.value
#> 1 1.832877e-05
#> 2 2.076965e-01
#> 3 3.721823e-01
#> 4 3.208012e-01
#> 5 9.561386e-03
#> 6 7.671335e-01
#> 7 3.802284e-03
#> 8 2.989200e-01
#> 9 1.555895e-01
pool_lm$multiparm_final
#> $`Step 4`
#> p-values D1 F-statistic
#> Smoking 0.5399398352 0.7214117
#> JobControl 0.3705279273 0.8045610
#> factor(Carrying) 0.0001017566 5.9155402
#> factor(Satisfaction) 0.0025183119 6.2392581
#> Smoking*factor(Carrying) 0.3318368885 1.1068101
pool_lm$predictors_out
#> Gender Smoking Function JobControl factor(Carrying)
#> Step 1 0 0 1 0 0
#> Step 2 0 0 0 0 0
#> Step 3 1 0 0 0 0
#> Removed 1 0 1 0 0
#> factor(Satisfaction) Smoking*factor(Carrying) Gender*Smoking
#> Step 1 0 0 0
#> Step 2 0 0 1
#> Step 3 0 0 0
#> Removed 0 0 1Back to Examples
Pooling linear regression models over 5 imputed datasets with BS using a p-value of 0.05 and as method D1. A spline predictor and interaction term are part of the selection procedure.
library(psfmi)
pool_lm <- psfmi_lm(data=lbpmilr, nimp=5, impvar="Impnr",
formula = Pain ~ Gender + Smoking +
JobControl + factor(Carrying) + factor(Satisfaction) +
factor(Carrying):Smoking + rcs(Function, 3),
method="D1",
p.crit=0.05, direction="BW")
#> Removed at Step 1 is - rcs(Function,3)
#> Removed at Step 2 is - Smoking*factor(Carrying)
#> Removed at Step 3 is - Smoking
#> Removed at Step 4 is - JobControl
#> Removed at Step 5 is - Gender
#>
#> Selection correctly terminated,
#> No more variables removed from the model
pool_lm$RR_model_final
#> $`Step 6`
#> term estimate std.error statistic df p.value
#> 1 (Intercept) 3.8156476 0.3621860 10.5350490 129.49014 4.010553e-19
#> 2 factor(Carrying)2 0.8759161 0.3761904 2.3283850 113.24274 2.166656e-02
#> 3 factor(Carrying)3 1.8001704 0.3746799 4.8045553 145.87249 3.811778e-06
#> 4 factor(Satisfaction)2 0.1385358 0.3729809 0.3714288 108.41273 7.110431e-01
#> 5 factor(Satisfaction)3 1.4420012 0.4685986 3.0772635 74.55846 2.921715e-03
pool_lm$multiparm_final
#> $`Step 6`
#> p-values D1 F-statistic
#> factor(Carrying) 1.752967e-05 11.125118
#> factor(Satisfaction) 2.477744e-03 6.275617
pool_lm$predictors_out
#> Gender Smoking JobControl factor(Carrying) factor(Satisfaction)
#> Step 1 0 0 0 0 0
#> Step 2 0 0 0 0 0
#> Step 3 0 1 0 0 0
#> Step 4 0 0 1 0 0
#> Step 5 1 0 0 0 0
#> Removed 1 1 1 0 0
#> rcs(Function,3) Smoking*factor(Carrying)
#> Step 1 1 0
#> Step 2 0 1
#> Step 3 0 0
#> Step 4 0 0
#> Step 5 0 0
#> Removed 1 1Back to Examples