README.md

In elbersb/weightedcontrasts: Orthogonal Polynomial Contrast Matrices for Unbalanced Data

weightedcontrasts

Provides the function contr.poly.weighted to apply orthogonal polynomial contrasts to unbalanced data. The function is general, but the examples are specific to age-period-cohort models. Currently, the package contains the following:

• The function contr.poly.weighted
• The dataset prostate from Holford 1983 (Table 2)
• A vignette that reanalyzes the example given in Holford 1983
• A vignette that reanalyzes the example given in Fosse and Winship 2019

Installation

You can install the development version:

remotes::install_github("elbersb/weightedcontrasts")

Example

This example shows how contr.poly.weighted provides a contrast matrix that will lead to an orthogonal design matrix, even if the data are unbalanced. We assume a situation in which an evenly-spaced predictor, such as age groups (e.g., 20-24, 25-29, 30-34, etc.).

library("weightedcontrasts")

# first, the balanced case
group <- factor(c(20, 20, 25, 25, 30, 30))
contrasts(group) <- contr.poly
X <- model.matrix(~ group)
zapsmall(crossprod(X)) # correct result
#>             (Intercept) group.L group.Q
#> (Intercept)           6       0       0
#> group.L               0       2       0
#> group.Q               0       0       2

# but in the unbalanced case, contr.poly fails
group <- factor(c(20, 20, 25, 25, 30))
contrasts(group) <- contr.poly
X <- model.matrix(~ group)
zapsmall(crossprod(X)) # wrong result!
#>             (Intercept)   group.L   group.Q
#> (Intercept)    5.000000 -0.707107 -0.408248
#> group.L       -0.707107  1.500000 -0.288675
#> group.Q       -0.408248 -0.288675  1.833333

# this is where contr.poly.weighted comes in
# (width specifies the width of the group intervals)
group <- factor(c(20, 20, 25, 25, 30))
contrasts(group) <- contr.poly.weighted(group, width = 5)
X <- model.matrix(~ group)
zapsmall(crossprod(X)) # correct result
#>             (Intercept) group.L group.Q
#> (Intercept)           5       0 0.00000
#> group.L               0      70 0.00000
#> group.Q               0       0 1.55556

References

Elbers, Benjamin. 2020. Orthogonal Polynomial Contrasts and Applications to Age-Period-Cohort Models, Working Paper.

Fosse, Ethan and Christopher Winship. 2019. Analyzing Age-Period-Cohort Data: A Review and Critique, Annual Review of Sociology 45:467–92.

Holford, Theodore R.. 1983. The Estimation of Age, Period and Cohort Effects for Vital Rates, Biometrics 39(2): 311-324.

elbersb/weightedcontrasts documentation built on Dec. 20, 2021, 4:15 a.m.