In R-Computing-Lab/discord: Functions for Discordant Kinship Modeling
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Introduction
Purpose
This vignette demonstrates how to incorporate categorical predictors in discordant-kinship regression analyses using the discord package. Building on dyadic modeling strategies from Kenny et al. [@kenny2006] and extensions to kinship models in our prior work [@Hwang2022], we present several approaches for incorporating categorical variables into these specialized regression models.
We focus on:
- How to code and interpret categorical variables at different levels (between-dyads vs. mixed)
- Methods for treating categorical predictors (binary match vs. multi-match)
- Practical implementation using the
discord package
To illustrate these concepts, we examine whether sex and race predict socioeconomic status (SES) at age 40, using different categorical coding schemes applied to data from the 1979 National Longitudinal Survey of Youth (NLSY79).
Understanding Variable Types in Dyadic Analysis
In dyadic analysis, categorical predictors can operate at different levels:
- Between-dyad variables: Variables that are constant within dyads.
- Example: For full siblings, race is often a between-dyad variable.
- Within-dyad variables: Variables that vary within dyads but remain constant across dyads (rare for categorical variables).
- Example: Division of chores between roommates (must sum to 100%)
- Mixed variables: Vary both within and across dyads
- Example: Biological sex in non-MZ twin siblings; age; personality traits
We summarize these distinctions below:
| Variable Type | Definition | Examples | Analytic Implications |
|---------------|------------|----------|----------------------|
| Between-dyads | Members of the same pair have identical values | Race in same-race siblings; Length of marriage in couples | Simplifies analysis; Functions like individual-level variable |
| Within-dyads | Varies within pairs but constant across pairs | Division of chores between roommates (must sum to 100%) | Rare for categorical variables; Requires specialized handling |
| Mixed | Varies both within and across pairs | Sex in sibling pairs; Age; Personality traits | Most complex; Requires transformation to dyad-level variables |
For continuous predictors, researchers typically compute mean and difference scores. However, as noted by Kenny et al. [@kenny2006], these calculations are not meaningful for categorical variables and should instead be replaced with appropriate coding strategies.
Coding Approaches for Categorical Variables
The discord package implements two primary coding strategies for categorical predictors:
-
Binary Match Coding: Creates a binary indicator of whether pairs match (1) or differ (0) on the categorical variable.
-
Multi-Match Coding: Retains specific category combinations
Binary Match Coding
Binary match coding creates a simple indicator of whether pairs match (1) or differ (0) on a categorical variable:
- Same-sex pairs (male-male or female-female) → 1
- Mixed-sex pairs (male-female) → 0
Use case: When the research question focuses on similarity versus difference, rather than effects of specific categories.
Multi-Match Coding
Multi-match coding retains specific category information:
- Male-male pairs → "MALE"
- Female-female pairs → "FEMALE"
- Mixed pairs → "mixed"
Use case: When distinct effects for specific categories are hypothesized (e.g., male pairs vs. female pairs).
Following Hwang and Garrison [@Hwang2022], the coding approach you select should align with your research questions and theoretical framework.
Data Preparation
We demonstrate how to handle categorical predictors using sibling data from the NLSY79. We begin by loading the necessary packages and preparing the dataset.
Package Loading and Data Setup
# Loading necessary packages and data
# For easy data manipulation
library(dplyr)
# For kinship linkages
library(NlsyLinks)
# For discordant-kinship regression
library(discord)
# pipe
library(magrittr)
# data
data(data_flu_ses)
We then filter and clean the dataset, create kinship links, and recode the categorical variables. This example uses full siblings (R = 0.5) from the Gen1 cohort.
# for reproducibility
set.seed(2023)
link_vars <- c("S00_H40", "RACE", "SEX")
# Specify NLSY database and kin relatedness
link_pairs <- Links79PairExpanded %>%
filter(RelationshipPath == "Gen1Housemates" & RFull == 0.5)
We use CreatePairLinksSingleEntered() from the NlsyLinks package to merge kinship links with our target variables. This merge creates a sibling-pair dataset in wide format. Suffixes distinguish the two individuals in each pair.
df_link <- CreatePairLinksSingleEntered(
outcomeDataset = data_flu_ses,
linksPairDataset = link_pairs,
outcomeNames = link_vars
)
To ensure the dependent variable (SES at age 40) is available for both siblings, we remove cases with missing values. We also recode sex and race into factors.
# We removed the pair when the Dependent Variable is missing.
df_link <- df_link %>%
filter(!is.na(S00_H40_S1) & !is.na(S00_H40_S2)) %>%
mutate(
SEX_S1 = case_when(
SEX_S1 == 0 ~ "MALE",
SEX_S1 == 1 ~ "FEMALE"
),
SEX_S2 = case_when(
SEX_S2 == 0 ~ "MALE",
SEX_S2 == 1 ~ "FEMALE"
),
RACE_S1 = case_when(
RACE_S1 == 0 ~ "NONMINORITY",
RACE_S1 == 1 ~ "MINORITY"
),
RACE_S2 = case_when(
RACE_S2 == 0 ~ "NONMINORITY",
RACE_S2 == 1 ~ "MINORITY"
)
)
For full siblings, race is a between-dyad variable. In this example, we restrict the analyses to same-race pairs.
df_link <- df_link %>%
dplyr::filter(RACE_S1 == RACE_S2)
To avoid violating assumptions of independence, we retain only one sibling pair per household:
df_link <- df_link %>%
group_by(ExtendedID) %>%
slice_sample() %>%
ungroup()
Handling Categorical Predictors
Mixed Variables: Sex as an Example
Sex is a classic example of a mixed variable in sibling studies because it can vary both within and between dyads. Siblings may be of the same or different sexes, and the composition varies across families.
We use the discord_data() function to prepare the data for analysis.
cat_sex <- discord_data(
data = df_link,
outcome = "S00_H40",
sex = "SEX",
race = "RACE",
demographics = "sex",
predictors = NULL,
pair_identifiers = c("_S1", "_S2"),
coding_method = "both"
)
In the restructured data, the individual with the higher SES (the dependent variable) is labeled "_1" and the other is labeled "_2". This gives us the following sex compositions:
cat_sex <- cat_sex %>%
dplyr::mutate(SEX_binarymatch = case_when(
SEX_binarymatch == 0 ~ "mixed-sex",
SEX_binarymatch == 1 ~ "same-sex"
))
cat_sex %>%
slice(1:500) %>%
slice_sample(n = 6) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling(full_width = FALSE)
The dataset contains the following sex pairings:
cat_sex %>%
group_by(SEX_1, SEX_2) %>%
summarize(n(), .groups = "drop") %>%
kableExtra::kbl("html", align = "c", col.names = c("SEX_1", "SEX_2", "sample_size")) %>%
kableExtra::kable_styling(full_width = FALSE)
By default, the SEX_1 variable indicates the sex of the individual who has the higher DV within the pair, and the SEX_2 variable indicates the sex of the other member of the dyad.
As shown, the discord_data() function generates both SEX_binarymatch and SEX_multimatch variables. This recodes the sex variable—which initially varied within and between dyads—into between-dyad variables:
cat_sex %>%
group_by(SEX_binarymatch, SEX_multimatch, SEX_1, SEX_2) %>%
summarize(n(), .groups = "drop") %>%
kableExtra::kbl("html", align = "c", col.names = c("binary", "multi", "SEX_1", "SEX_2", "sample_size")) %>%
kableExtra::kable_styling(full_width = FALSE)
Researchers can choose between these options depending on their research question:
- Use SEX_binarymatch when comparing same-sex and mixed-sex pairs.
- Use SEX_multimatch when comparing male-male, female-female, and mixed-sex pairs.
Between-dyad Variable: Race as an Example
For demonstration purposes, we have already restricted the dataset to include only same-race pairs, making race a between-dyad variable. We now prepare the data specifically for testing whether there are racial differences in SES discordance.
set.seed(2023) # for reproducibility
# Prepare data with race as demographic variable
cat_race <- discord_data(
data = df_link,
outcome = "S00_H40",
predictors = NULL,
sex = "SEX",
race = "RACE",
demographics = "race",
pair_identifiers = c("_S1", "_S2"),
coding_method = "both"
)
The race compositions in the dataset are as follows:
cat_race <- cat_race %>%
dplyr::mutate(RACE_binarymatch = case_when(
RACE_binarymatch == 0 ~ "mixed-race",
RACE_binarymatch == 1 ~ "same-race"
))
cat_race %>%
group_by(RACE_binarymatch, RACE_multimatch, RACE_1, RACE_2) %>%
summarize(n(), .groups = "drop") %>%
kableExtra::kbl("html",
align = "c",
col.names = c("RACE_binarymatch", "RACE_multimatch", "RACE_1", "RACE_2", "sample_size")
) %>%
kableExtra::kable_styling(full_width = FALSE)
Because we filtered for same-race pairs, all pairs have RACE_binarymatch = "same-race." When using NLSY data, the RACE_multimatch variable distinguishes between the three categories used by the Bureau of Labor Statistics (Black, Hispanic, and Non-Black, Non-Hispanic).
The RACE_binarymatch variable indicates whether the pair is same-race or mixed-race. As all pairs are same-race in this sample, this variable does not vary. The RACE_multimatch variable classifies pairs into one of three categories:
The RACE_binarymatch variable indicates whether the pair is same-race or mixed-race. As all pairs are same-race in this sample, this variable does not vary. The RACE_multimatch variable classifies pairs into one of three categories:
Since we filtered for same-race pairs only, all pairs have RACE_binarymatch = "same-race". When using NLSY data, the RACE_multimatch variable distinguishes between the three groupings that the bureau of labor statistics uses (Black, Hispanic, and Non-Black, Non-Hispanic).
The RACE_binarymatch variable indicates whether the pair is the same-race pair or mixed-race pair .As all pairs are same-race in this sample, this variable does not vary within dyad. The RACE_multimatch The RACE_multimatch variable classifies pairs into one of three categories:
- Minority-minority,
-
Nonminority-nonminority,
-
Discordant (unused in this restricted sample).
Combining Binary and Multi-match Variables
We can also prepare data that includes multiple demographic variables.
# for reproducibility
set.seed(2023)
cat_both <- discord_data(
data = df_link,
outcome = "S00_H40",
predictors = NULL,
sex = "SEX",
race = "RACE",
demographics = "both",
pair_identifiers = c("_S1", "_S2"),
coding_method = "both"
)
The demographic variables can be used in the same regression model.
cat_both <- cat_both %>%
dplyr::mutate(
RACE_binarymatch = case_when(
RACE_binarymatch == 0 ~ "mixed-race",
RACE_binarymatch == 1 ~ "same-race"
),
SEX_binarymatch = case_when(
SEX_binarymatch == 0 ~ "mixed-sex",
SEX_binarymatch == 1 ~ "same-sex"
)
)
cat_both %>%
group_by(RACE_multimatch, RACE_1, RACE_2, SEX_binarymatch, SEX_multimatch, SEX_1, SEX_2) %>%
summarize(n(), .groups = "drop") %>%
kableExtra::kbl("html",
align = "c",
col.names = c(
"RACE_multi", "RACE_1", "RACE_2", "SEX_binary", "SEX_multi", "SEX_1", "SEX_2",
"sample_size"
)
) %>%
kableExtra::kable_styling(full_width = FALSE)
In this table:
-
RACE_multimatch shows whether pairs are minority-minority or nonminority-nonminority.
-
SEX_binarymatch distinguishes same-sex and mixed-sex pairs.
-
SEX_multimatch identifies male-male, female-female, and mixed-sex pairings.
Results and Interpretation
Regression Analysis: Sex Variables
Binary Match Coding for Sex
First, we test whether same-sex versus mixed-sex pairs differ in SES discordance.
The regression model can be conducted as such:
discord_sex_binary <- discord_regression(
data = df_link,
outcome = "S00_H40",
sex = "SEX",
race = "RACE",
demographics = "sex",
predictors = NULL,
pair_identifiers = c("_S1", "_S2"),
coding_method = "binary"
)
discord_sex_binary %>%
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
We predict sibling differences in SES (S00_H40_diff).
-
The mean SES score (S00_H40_mean) is a significant control variable (p =r round(summary(discord_sex_binary)[["coefficients"]]["S00_H40_mean", "Pr(>|t|)"],3)). S00_H40_mean is negatively associated with the difference in SES score between siblings at age 40, controlling for another variable (in this case, SEX_binarymatch). For one unit increase of S00_H40_mean, S00_H40_diffis expected to decrease approximately r round(discord_sex_binary[["coefficients"]][["S00_H40_mean"]],3).
-
The binary sex match variable SEX_binarymatch is not a significant predictor (p = r round(summary(discord_sex_binary)[["coefficients"]]["SEX_binarymatch", "Pr(>|t|)"],3)), when controlling for S00_H40_mean. There is no significant differences between same-sex pairs and mixed-sex pairs in S00_H40_diff. This means that the difference between same-sex pairs and mixed-sex pairs does not significantly predict the S00_H40_diff in the pair when controlling for S00_H40_mean.
Multi-Match Coding for Sex
Next, we examine whether male-male, female-female, and mixed-sex pairs differ in SES discordance.
The regression model can be conducted as such:
discord_sex_multi <- discord_regression(
data = df_link,
outcome = "S00_H40",
sex = "SEX",
race = "RACE",
predictors = NULL,
pair_identifiers = c("_S1", "_S2"),
coding_method = "multi"
)
discord_sex_multi %>%
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
-
The term S00_H40_mean was a significant control variable (p = r round(summary(discord_sex_multi)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3)). This means that the mean SES score for the sibling pairs (S00_H40_mean) is negatively associated with the difference in SES between siblings (S00_H40_diff), controlling for other variables (in this case, SEX_multimatch). It is estimated that for one unit increase of S00_H40_mean, S00_H40_diff is expected to decrease approximately r abs(round(discord_sex_multi[["coefficients"]][["S00_H40_mean"]],3)).
-
There was no significant difference between female-female pairs and male-male pairs (p=r round(summary(discord_sex_multi)[["coefficients"]]["SEX_multimatchMALE", "Pr(>|t|)"],3)) to predict S00_H40_diff. Similarly, there were no significant differences between mixed-sex pairs and female-female pairs (p = r round(summary(discord_sex_multi)[["coefficients"]]["SEX_multimatchmixed", "Pr(>|t|)"],3)).
-
The coefficient r abs(round(discord_sex_multi[["coefficients"]][["SEX_multimatchMALE"]],3)) is the difference between the expected S00_H40_diff for the reference group (in this case, the female-female pairs) and the male-male pairs.
-
The coefficient r abs(round(discord_sex_multi[["coefficients"]][["SEX_multimatchmixed"]],3)) is the difference between the expected S00_H40_diff for the reference group (in this case, the female-female pairs) and the mixed-sex pairs. However, these coefficients are not significant, so it is not advisable to interpret the coefficients.
Mean SES Model with Sex
We can also examine whether sex composition predicts mean SES levels (rather than SES differences):
discord_cat_mean <- lm(S00_H40_mean ~ SEX_binarymatch,
data = cat_sex
)
discord_cat_mean %>%
# for nicer regression output
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
In this regression model, the mean SES score for the siblings (S00_H40_mean) was regressed on the SEX-composition variable (SEX_binarymatch).
There is no significant difference between same-sex pairs and mixed-sex pairs in the mean SES score for the siblings (p=r round(summary(discord_cat_mean)[["coefficients"]]["SEX_binarymatchsame-sex", "Pr(>|t|)"],3))
It is estimated that compared to the mixed-sex pairs, the same-sex pairs would have approximately r abs(round(discord_cat_mean[["coefficients"]][["SEX_binarymatchsame-sex"]],3)) higher S00_H40_mean. However, this coefficient is not significant, so it is not advisable to interpret the coefficient.
Multi-Match Coding for Sex
discord_cat_mean2 <- lm(S00_H40_mean ~ SEX_multimatch,
data = cat_sex
)
discord_cat_mean2 %>%
# for nicer regression output
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
There is a significant difference between female-female pairs and male-male pairs (r round(summary(discord_cat_mean2)[["coefficients"]]["SEX_multimatchMALE", "Pr(>|t|)"],3)) to predict the S00_H40_mean. However, there is no significant difference between mixed-sex pairs and female-female pairs (p = r round(summary(discord_cat_mean2)[["coefficients"]]["SEX_multimatchmixed", "Pr(>|t|)"],3)).
The coefficient r abs(round(discord_cat_mean2[["coefficients"]]["SEX_multimatchMALE"],3)) is the difference between the expected S00_H40_mean (the mean SES score for the siblings) for the reference group (in this case, the female-female pairs) and the male-male pairs. It can be concluded that male-male pairs and female-female pair has significant differences in S00_H40_mean.
The coefficient r abs(round(discord_cat_mean2[["coefficients"]]["SEX_multimatchmixed"],3)) is the difference between the expected S00_H40_mean for the reference group (in this case, the female-female pairs) and the mixed-sex pairs. However, these coefficients are not significant, so it is not advisable to interpret the coefficients.
Regression Analysis: Race Variables
For race variables, we use the multi-match coding to examine differences between minority and non-minority pairs:
Multimatch
The regression model with a multi-match race variable as a predictor can be conducted as such:
# perform kinship regressions
cat_race_reg <- discord_regression(
data = df_link,
outcome = "S00_H40",
sex = "SEX",
race = "RACE",
demographics = "race",
predictors = NULL,
pair_identifiers = c("_S1", "_S2"),
coding_method = "multi"
)
cat_race_reg %>%
# for nicer regression output
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The mean SES score for the siblings (S00_H40_mean) is a significant control variable (p =r round(summary(cat_race_reg)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3). The term S00_H40_mean is negatively associated with the difference score of SES between siblings (S00_H40_diff), controlling for another variable (in this case, RACE_multimatchNONMINORITY). It is estimated that for one unit increase of S00_H40_mean, the DV (S00_H40_diff) is expected to decrease by approximately
r abs(round(cat_race_reg[["coefficients"]][["S00_H40_mean"]],3)).
The term RACE_multimatchNONMINORITY was a significant predictor of S00_H40_diff (p = r round(summary(cat_race_reg)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)) after controlling for S00_H40_mean. This means that the difference between the "Minority-minority" sibling pairs and "nonminority-non-minority" sibling pairs significantly predicts S00_H40_diff. Specifically, compared to the reference group (the "minority" pairs), "nonminority" pairs are expected to have approximately r abs(round(cat_race_reg[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) lower S00_H40_diff.
Mean SES Model with Race
We can also examine whether race composition predicts mean SES levels:
discord_cat_mean <- lm(S00_H40_mean ~ RACE_multimatch,
data = cat_race
)
discord_cat_mean %>%
# for nicer regression output
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
There is significant difference between "minority" pairs and "nonminority" pairs in S00_H40_mean (p =r round(summary(discord_cat_mean)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)).
It is estimated that, compared to the reference group (minority pairs), the nonminority pairs would have approximately
r abs(round(discord_cat_mean[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) lower S00_H40_mean.
Regression Analysis: Combined Sex and Race Variables
We can include both sex and race as predictors in the same model:
Like before we restructure the data for the kinship-discordant regression, but this time we using the discord_regression() function, which calls the discord_data() function internally.
Multimatch
both_multi <- discord_regression(
data = df_link,
outcome = "S00_H40",
sex = "SEX",
race = "RACE",
demographics = "both",
predictors = NULL,
pair_identifiers = c("_S1", "_S2"),
coding_method = "multi"
)
both_multi %>%
# for nicer regression output
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation
The mean SES score for the siblings (S00_H40_mean) is a significant control variable (p = r round(summary(both_multi)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3) ). S00_H40_mean is negatively associated with the difference score of SES between the siblings (S00_H40_diff), controlling for other variables (in this case, the SEX_multimatchMALE, SEX_multimatchmixed and RACE_multimatchNONMINORITY). It is estimated that for one unit increase of the mean SES score for the sibling pairs( S00_H40_mean), the difference score of SES between siblings(S00_H40_diff) is expected to decrease approximately r round(both_multi[["coefficients"]][["S00_H40_mean"]],3).
The SEX_multimatchmixed and SEX_multimatchMALE are not significant predictors when controlling for other variables (i.e., S00_H40_mean and RACE_multimatchNONMINORITY). The coefficient r round(both_multi[["coefficients"]][["SEX_multimatchMALE"]],3) is the difference between the expected DV (S00_H40_diff) for the reference group (in this case, the "female-female" pairs) and the "male-male" pairs. The coefficient r round(both_multi[["coefficients"]][["SEX_multimatchmixed"]],3) is the difference between the expected DV (S00_H40_diff) for the female-female pairs and the mixed-sex pairs. However, these coefficients are not significant, so it is not advisable to interpret the coefficients.
The term RACE_multimatchNONMINORITY is a significant predictor (p = r round(summary(both_multi)[["coefficients"]]["RACE_multimatchNONMINORITY", "Pr(>|t|)"],3)) when controlling for other variables (i.e., SEX_multimatchMALE, SEX_multimatchmixed, and S00_H40_mean). This means that there is a significant difference between minority race pairs and nonminority race pairs in the difference score of SES between siblings (S00_H40_diff) when controlling for the model covariates (i.e., SEX_multimatchMALE, SEX_multimatchmixed, and S00_H40_mean). Specifically, compared to the minority race pairs, the nonminority race pairs were expected to have approximately r round(both_multi[["coefficients"]][["RACE_multimatchNONMINORITY"]],3) higher difference score of SES between siblings at age 40.
Alternative Model: Binary Sex Match and Multi-Match Race
To combine binary and multi-match coding approaches, we can use the standard lm() function:
We can perform regression using the binary-match sex variable and multi-match race variable as such:
discord_cat_diff <- lm(
S00_H40_diff ~ S00_H40_mean +
RACE_multimatch + SEX_binarymatch,
data = cat_both
)
# for nicer regression output
discord_cat_diff %>%
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The mean SES score for the siblings at 40 (S00_H40_mean) is a significant control variable (p =
r round(summary(discord_cat_diff)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3). The mean SES score for the siblings (S00_H40_mean) is negatively associated with the difference score of SES between the siblings (S00_H40_diff), controlling for other variables (in this case, SEX_binarymatchsame-sex and RACE_multimatchNONMINORITY). It is estimated that for one unit increase of S00_H40_mean, the DV (S00_H40_diff) is expected to decrease approximately r abs(round(discord_cat_diff[["coefficients"]][["S00_H40_mean"]],3)).
The term SEX_binarymatchsame-sex is not a significant predictor (p = r round(summary(discord_cat_diff)[["coefficients"]][["SEX_binarymatchsame-sex", "Pr(>|t|)"]],3)) when controlling for other variables (i.e., S00_H40_mean and RACE_multimatchNONMINORITY). This means that the difference between same-sex pairs and mixed-sex pairs does not significantly predict the difference score of SES between siblings (S00_H40_diff) when controlling for the mean SES score for the siblings (S00_H40_mean) and race-composition of the pair (RACE_multimatchNONMINORITY). Compared to the mixed-sex pairs, it is estimated that the same-sex pairs have approximately r abs(round(discord_cat_diff[["coefficients"]][["SEX_binarymatchsame-sex"]],3))higher difference score of SES between siblings (S00_H40_diff) when controlling for the mean SES score for the sibling pairs (S00_H40_mean) and race-composition of the pairs (RACE_multimatchNONMINORITY). However, this coefficient is not statistically significant and should not be interpreted.
The term RACE_multimatchNONMINORITYis a significant predictor (p = r round(summary(discord_cat_diff)[["coefficients"]][["RACE_multimatchNONMINORITY", "Pr(>|t|)"]],3)). This means that there is a significant difference between minority race pairs and nonminority race pairs to predict the difference score of SES between the siblings (S00_H40_diff) when controlling for the model covariates (i.e., SEX_binarymatchsame-sex and S00_H40_mean). Specifically, compared to the minority race pairs, nonminority race pairs were expected to have approximately r abs(round(discord_cat_diff[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) lower difference scores of SES between siblings (S00_H40_diff).
Mean SES Models with Both Variables
Finally, we examine how sex and race together predict mean SES levels:
discord_cat_mean <- lm(
S00_H40_mean ~ RACE_multimatch +
SEX_multimatch,
data = cat_both
)
discord_cat_mean %>%
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The term SEX_multimatchMALE is a significant predictor (p = r round(summary(discord_cat_mean)[["coefficients"]]["SEX_multimatchMALE","Pr(>|t|)"],3)) when controlling for other variables (i.e., SEX_multimatchmixedand RACEe_multimatchNONMINORITY). This means that the difference between female-female pairs and male-male pairs significantly predicted the mean SES score for the siblings when controlling for race-composition of the pairs. Compared to the female-female pairs, it is estimated that the male-male pairs have approximately
r abs(round(discord_cat_mean[["coefficients"]][["SEX_multimatchMALE"]],3)) higher mean SES score for the siblings when controlling for and race-composition of the pairs.
The term SEX_multimatchmixed was not a significant predictor (p = r round(summary(discord_cat_mean)[["coefficients"]]["SEX_multimatchmixed","Pr(>|t|)"],3)) when controlling for other variables (i.e., SEX_multimatchMALEand RACE_multimatchNONMINORITY). This means that the difference between female-female pairs and mixed-sex pairs does not significantly predict the mean SES score for the siblings when controlling for race-composition of the pairs. Compared to the female-female pairs, it is estimated that the mixed-sex pairs have approximately
r abs(round(discord_cat_mean[["coefficients"]][["SEX_multimatchmixed"]],3)) higher mean SES score for the sibling pairs when controlling for and race-composition of the pairs. However, this variable is not significant, so it is not advisable to interpret the coefficient.
The term RACE_multimatchNONMINORITY is a significant predictor (p = r round(summary(discord_cat_mean)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)). This means that there is a significant difference between minority race pairs and nonminority race pairs in the mean SES score for the sibling pairs (S00_H40_mean) when controlling for the other variables (i.e., SEX_multimatchmixed and SEX_multimatchMALE). Specifically, compared to the minority race pairs, nonminority race pairs were expected to have approximately r abs(round(discord_cat_mean[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) higher mean SES score for siblings
Mean SES Models with Combining multimatch and binarymatch
discord_cat_mean2 <- lm(S00_H40_mean ~ RACE_multimatch + SEX_binarymatch,
data = cat_both
)
discord_cat_mean2 %>%
broom::tidy() %>%
mutate(
p.value = scales::pvalue(p.value, add_p = TRUE),
across(.cols = where(is.numeric), ~ round(.x, 3))
) %>%
rename(
"Standard Error" = std.error,
"T Statistic" = statistic
) %>%
rename_with(~ snakecase::to_title_case(.x)) %>%
kableExtra::kbl("html", align = "c") %>%
kableExtra::kable_styling() %>%
kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The term SEX_binarymatchsame-sex is not a significant predictor (p = r round(summary(discord_cat_mean2)[["coefficients"]]["SEX_binarymatchsame-sex","Pr(>|t|)"],3)) when controlling for the race-composition variable (i.e., RACE_multimatchNONMINORITY). This means that the difference between mixed-sex pairs and same sex pairs does not significantly predict the mean SES score for the siblings when controlling for race-composition of the pairs. Compared to the mixed-sex pairs, it is estimated that the same-sex pairs have approximately
r abs(round(discord_cat_mean2[["coefficients"]][["SEX_binarymatchsame-sex"]],3)) higher mean SES score for the sibling pairs (S00_H40_mean) when controlling for and race-composition of the pairs (RACE_multimatchNONMINORITY). However, this variable is not significant, so it is not advisable to interpret the coefficient.
The term RACE_multimatchNONMINORITY is a significant predictor (p = r round(summary(discord_cat_mean2)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)). This means that there is a significant difference between minority race pairs and nonminority race pairs in the the mean SES score for the siblings when controlling for the sex-composition variable (i.e., SEX_binarymatchsame-sex). Specifically, compared to the minority race pairs, nonminority race pairs were expected to have approximately r abs(round(discord_cat_mean2[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) higher mean SES score for siblings
Conclusion
This vignette has demonstrated how to incorporate categorical predictors in discordant-kinship regression analyses using the discord package.
Key findings and recommendations include:
- Variable Type Matters: Categorical variables must be handled differently depending on whether they are between-dyads variables (like race in our filtered sample) or mixed variables (like sex in sibling pairs).
- Coding Approaches Offer Different Insights:
- Binary match coding examines whether similarity/difference matters
- Multi-match coding allows for more detailed examination of specific category effects
Implementation Recommendations:
For implementation in your own research, we recommend:
- Consider the theoretical nature of your categorical predictors
- Use discord_data() to prepare categorical variables appropriately
- Choose coding schemes based on your specific research questions
- Carefully interpret results in light of variable coding decisions
References
R-Computing-Lab/discord documentation built on June 9, 2025, 3:57 p.m.
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knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) options(rmarkdown.html_vignette.check_title = FALSE)
Introduction
Purpose
This vignette demonstrates how to incorporate categorical predictors in discordant-kinship regression analyses using the discord package. Building on dyadic modeling strategies from Kenny et al. [@kenny2006] and extensions to kinship models in our prior work [@Hwang2022], we present several approaches for incorporating categorical variables into these specialized regression models.
We focus on:
- How to code and interpret categorical variables at different levels (between-dyads vs. mixed)
- Methods for treating categorical predictors (binary match vs. multi-match)
- Practical implementation using the
discordpackage
To illustrate these concepts, we examine whether sex and race predict socioeconomic status (SES) at age 40, using different categorical coding schemes applied to data from the 1979 National Longitudinal Survey of Youth (NLSY79).
Understanding Variable Types in Dyadic Analysis
In dyadic analysis, categorical predictors can operate at different levels:
- Between-dyad variables: Variables that are constant within dyads.
- Example: For full siblings, race is often a between-dyad variable.
- Within-dyad variables: Variables that vary within dyads but remain constant across dyads (rare for categorical variables).
- Example: Division of chores between roommates (must sum to 100%)
- Mixed variables: Vary both within and across dyads
- Example: Biological sex in non-MZ twin siblings; age; personality traits
We summarize these distinctions below:
| Variable Type | Definition | Examples | Analytic Implications | |---------------|------------|----------|----------------------| | Between-dyads | Members of the same pair have identical values | Race in same-race siblings; Length of marriage in couples | Simplifies analysis; Functions like individual-level variable | | Within-dyads | Varies within pairs but constant across pairs | Division of chores between roommates (must sum to 100%) | Rare for categorical variables; Requires specialized handling | | Mixed | Varies both within and across pairs | Sex in sibling pairs; Age; Personality traits | Most complex; Requires transformation to dyad-level variables |
For continuous predictors, researchers typically compute mean and difference scores. However, as noted by Kenny et al. [@kenny2006], these calculations are not meaningful for categorical variables and should instead be replaced with appropriate coding strategies.
Coding Approaches for Categorical Variables
The discord package implements two primary coding strategies for categorical predictors:
-
Binary Match Coding: Creates a binary indicator of whether pairs match (1) or differ (0) on the categorical variable.
-
Multi-Match Coding: Retains specific category combinations
Binary Match Coding
Binary match coding creates a simple indicator of whether pairs match (1) or differ (0) on a categorical variable: - Same-sex pairs (male-male or female-female) → 1 - Mixed-sex pairs (male-female) → 0
Use case: When the research question focuses on similarity versus difference, rather than effects of specific categories.
Multi-Match Coding
Multi-match coding retains specific category information:
- Male-male pairs → "MALE"
- Female-female pairs → "FEMALE"
- Mixed pairs → "mixed"
Use case: When distinct effects for specific categories are hypothesized (e.g., male pairs vs. female pairs).
Following Hwang and Garrison [@Hwang2022], the coding approach you select should align with your research questions and theoretical framework.
Data Preparation
We demonstrate how to handle categorical predictors using sibling data from the NLSY79. We begin by loading the necessary packages and preparing the dataset.
Package Loading and Data Setup
# Loading necessary packages and data # For easy data manipulation library(dplyr) # For kinship linkages library(NlsyLinks) # For discordant-kinship regression library(discord) # pipe library(magrittr) # data data(data_flu_ses)
We then filter and clean the dataset, create kinship links, and recode the categorical variables. This example uses full siblings (R = 0.5) from the Gen1 cohort.
# for reproducibility set.seed(2023) link_vars <- c("S00_H40", "RACE", "SEX") # Specify NLSY database and kin relatedness link_pairs <- Links79PairExpanded %>% filter(RelationshipPath == "Gen1Housemates" & RFull == 0.5)
We use CreatePairLinksSingleEntered() from the NlsyLinks package to merge kinship links with our target variables. This merge creates a sibling-pair dataset in wide format. Suffixes distinguish the two individuals in each pair.
df_link <- CreatePairLinksSingleEntered( outcomeDataset = data_flu_ses, linksPairDataset = link_pairs, outcomeNames = link_vars )
To ensure the dependent variable (SES at age 40) is available for both siblings, we remove cases with missing values. We also recode sex and race into factors.
# We removed the pair when the Dependent Variable is missing. df_link <- df_link %>% filter(!is.na(S00_H40_S1) & !is.na(S00_H40_S2)) %>% mutate( SEX_S1 = case_when( SEX_S1 == 0 ~ "MALE", SEX_S1 == 1 ~ "FEMALE" ), SEX_S2 = case_when( SEX_S2 == 0 ~ "MALE", SEX_S2 == 1 ~ "FEMALE" ), RACE_S1 = case_when( RACE_S1 == 0 ~ "NONMINORITY", RACE_S1 == 1 ~ "MINORITY" ), RACE_S2 = case_when( RACE_S2 == 0 ~ "NONMINORITY", RACE_S2 == 1 ~ "MINORITY" ) )
For full siblings, race is a between-dyad variable. In this example, we restrict the analyses to same-race pairs.
df_link <- df_link %>% dplyr::filter(RACE_S1 == RACE_S2)
To avoid violating assumptions of independence, we retain only one sibling pair per household:
df_link <- df_link %>% group_by(ExtendedID) %>% slice_sample() %>% ungroup()
Handling Categorical Predictors
Mixed Variables: Sex as an Example
Sex is a classic example of a mixed variable in sibling studies because it can vary both within and between dyads. Siblings may be of the same or different sexes, and the composition varies across families.
We use the discord_data() function to prepare the data for analysis.
cat_sex <- discord_data( data = df_link, outcome = "S00_H40", sex = "SEX", race = "RACE", demographics = "sex", predictors = NULL, pair_identifiers = c("_S1", "_S2"), coding_method = "both" )
In the restructured data, the individual with the higher SES (the dependent variable) is labeled "_1" and the other is labeled "_2". This gives us the following sex compositions:
cat_sex <- cat_sex %>% dplyr::mutate(SEX_binarymatch = case_when( SEX_binarymatch == 0 ~ "mixed-sex", SEX_binarymatch == 1 ~ "same-sex" )) cat_sex %>% slice(1:500) %>% slice_sample(n = 6) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling(full_width = FALSE)
The dataset contains the following sex pairings:
cat_sex %>% group_by(SEX_1, SEX_2) %>% summarize(n(), .groups = "drop") %>% kableExtra::kbl("html", align = "c", col.names = c("SEX_1", "SEX_2", "sample_size")) %>% kableExtra::kable_styling(full_width = FALSE)
By default, the SEX_1 variable indicates the sex of the individual who has the higher DV within the pair, and the SEX_2 variable indicates the sex of the other member of the dyad.
As shown, the discord_data() function generates both SEX_binarymatch and SEX_multimatch variables. This recodes the sex variable—which initially varied within and between dyads—into between-dyad variables:
cat_sex %>% group_by(SEX_binarymatch, SEX_multimatch, SEX_1, SEX_2) %>% summarize(n(), .groups = "drop") %>% kableExtra::kbl("html", align = "c", col.names = c("binary", "multi", "SEX_1", "SEX_2", "sample_size")) %>% kableExtra::kable_styling(full_width = FALSE)
Researchers can choose between these options depending on their research question:
- Use SEX_binarymatch when comparing same-sex and mixed-sex pairs.
- Use SEX_multimatch when comparing male-male, female-female, and mixed-sex pairs.
Between-dyad Variable: Race as an Example
For demonstration purposes, we have already restricted the dataset to include only same-race pairs, making race a between-dyad variable. We now prepare the data specifically for testing whether there are racial differences in SES discordance.
set.seed(2023) # for reproducibility # Prepare data with race as demographic variable cat_race <- discord_data( data = df_link, outcome = "S00_H40", predictors = NULL, sex = "SEX", race = "RACE", demographics = "race", pair_identifiers = c("_S1", "_S2"), coding_method = "both" )
The race compositions in the dataset are as follows:
cat_race <- cat_race %>% dplyr::mutate(RACE_binarymatch = case_when( RACE_binarymatch == 0 ~ "mixed-race", RACE_binarymatch == 1 ~ "same-race" )) cat_race %>% group_by(RACE_binarymatch, RACE_multimatch, RACE_1, RACE_2) %>% summarize(n(), .groups = "drop") %>% kableExtra::kbl("html", align = "c", col.names = c("RACE_binarymatch", "RACE_multimatch", "RACE_1", "RACE_2", "sample_size") ) %>% kableExtra::kable_styling(full_width = FALSE)
Because we filtered for same-race pairs, all pairs have RACE_binarymatch = "same-race." When using NLSY data, the RACE_multimatch variable distinguishes between the three categories used by the Bureau of Labor Statistics (Black, Hispanic, and Non-Black, Non-Hispanic).
The RACE_binarymatch variable indicates whether the pair is same-race or mixed-race. As all pairs are same-race in this sample, this variable does not vary. The RACE_multimatch variable classifies pairs into one of three categories:
The RACE_binarymatch variable indicates whether the pair is same-race or mixed-race. As all pairs are same-race in this sample, this variable does not vary. The RACE_multimatch variable classifies pairs into one of three categories:
Since we filtered for same-race pairs only, all pairs have RACE_binarymatch = "same-race". When using NLSY data, the RACE_multimatch variable distinguishes between the three groupings that the bureau of labor statistics uses (Black, Hispanic, and Non-Black, Non-Hispanic).
The RACE_binarymatch variable indicates whether the pair is the same-race pair or mixed-race pair .As all pairs are same-race in this sample, this variable does not vary within dyad. The RACE_multimatch The RACE_multimatch variable classifies pairs into one of three categories:
- Minority-minority,
-
Nonminority-nonminority,
-
Discordant (unused in this restricted sample).
Combining Binary and Multi-match Variables
We can also prepare data that includes multiple demographic variables.
# for reproducibility set.seed(2023) cat_both <- discord_data( data = df_link, outcome = "S00_H40", predictors = NULL, sex = "SEX", race = "RACE", demographics = "both", pair_identifiers = c("_S1", "_S2"), coding_method = "both" )
The demographic variables can be used in the same regression model.
cat_both <- cat_both %>% dplyr::mutate( RACE_binarymatch = case_when( RACE_binarymatch == 0 ~ "mixed-race", RACE_binarymatch == 1 ~ "same-race" ), SEX_binarymatch = case_when( SEX_binarymatch == 0 ~ "mixed-sex", SEX_binarymatch == 1 ~ "same-sex" ) )
cat_both %>% group_by(RACE_multimatch, RACE_1, RACE_2, SEX_binarymatch, SEX_multimatch, SEX_1, SEX_2) %>% summarize(n(), .groups = "drop") %>% kableExtra::kbl("html", align = "c", col.names = c( "RACE_multi", "RACE_1", "RACE_2", "SEX_binary", "SEX_multi", "SEX_1", "SEX_2", "sample_size" ) ) %>% kableExtra::kable_styling(full_width = FALSE)
In this table:
-
RACE_multimatchshows whether pairs are minority-minority or nonminority-nonminority. -
SEX_binarymatchdistinguishes same-sex and mixed-sex pairs. -
SEX_multimatchidentifies male-male, female-female, and mixed-sex pairings.
Results and Interpretation
Regression Analysis: Sex Variables
Binary Match Coding for Sex
First, we test whether same-sex versus mixed-sex pairs differ in SES discordance.
The regression model can be conducted as such:
discord_sex_binary <- discord_regression( data = df_link, outcome = "S00_H40", sex = "SEX", race = "RACE", demographics = "sex", predictors = NULL, pair_identifiers = c("_S1", "_S2"), coding_method = "binary" )
discord_sex_binary %>% broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
We predict sibling differences in SES (S00_H40_diff).
-
The mean SES score (
S00_H40_mean) is a significant control variable (p =r round(summary(discord_sex_binary)[["coefficients"]]["S00_H40_mean", "Pr(>|t|)"],3)).S00_H40_meanis negatively associated with the difference in SES score between siblings at age 40, controlling for another variable (in this case,SEX_binarymatch). For one unit increase ofS00_H40_mean,S00_H40_diffis expected to decrease approximatelyr round(discord_sex_binary[["coefficients"]][["S00_H40_mean"]],3). -
The binary sex match variable
SEX_binarymatchis not a significant predictor (p =r round(summary(discord_sex_binary)[["coefficients"]]["SEX_binarymatch", "Pr(>|t|)"],3)), when controlling forS00_H40_mean. There is no significant differences between same-sex pairs and mixed-sex pairs inS00_H40_diff. This means that the difference between same-sex pairs and mixed-sex pairs does not significantly predict theS00_H40_diffin the pair when controlling forS00_H40_mean.
Multi-Match Coding for Sex
Next, we examine whether male-male, female-female, and mixed-sex pairs differ in SES discordance.
The regression model can be conducted as such:
discord_sex_multi <- discord_regression( data = df_link, outcome = "S00_H40", sex = "SEX", race = "RACE", predictors = NULL, pair_identifiers = c("_S1", "_S2"), coding_method = "multi" )
discord_sex_multi %>% broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
-
The term
S00_H40_meanwas a significant control variable (p =r round(summary(discord_sex_multi)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3)). This means that the mean SES score for the sibling pairs (S00_H40_mean) is negatively associated with the difference in SES between siblings (S00_H40_diff), controlling for other variables (in this case,SEX_multimatch). It is estimated that for one unit increase ofS00_H40_mean,S00_H40_diffis expected to decrease approximatelyr abs(round(discord_sex_multi[["coefficients"]][["S00_H40_mean"]],3)). -
There was no significant difference between female-female pairs and male-male pairs (p=
r round(summary(discord_sex_multi)[["coefficients"]]["SEX_multimatchMALE", "Pr(>|t|)"],3)) to predictS00_H40_diff. Similarly, there were no significant differences between mixed-sex pairs and female-female pairs (p =r round(summary(discord_sex_multi)[["coefficients"]]["SEX_multimatchmixed", "Pr(>|t|)"],3)). -
The coefficient
r abs(round(discord_sex_multi[["coefficients"]][["SEX_multimatchMALE"]],3))is the difference between the expectedS00_H40_difffor the reference group (in this case, the female-female pairs) and the male-male pairs. -
The coefficient
r abs(round(discord_sex_multi[["coefficients"]][["SEX_multimatchmixed"]],3))is the difference between the expectedS00_H40_difffor the reference group (in this case, the female-female pairs) and the mixed-sex pairs. However, these coefficients are not significant, so it is not advisable to interpret the coefficients.
Mean SES Model with Sex
We can also examine whether sex composition predicts mean SES levels (rather than SES differences):
discord_cat_mean <- lm(S00_H40_mean ~ SEX_binarymatch, data = cat_sex )
discord_cat_mean %>% # for nicer regression output broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
In this regression model, the mean SES score for the siblings (S00_H40_mean) was regressed on the SEX-composition variable (SEX_binarymatch).
There is no significant difference between same-sex pairs and mixed-sex pairs in the mean SES score for the siblings (p=r round(summary(discord_cat_mean)[["coefficients"]]["SEX_binarymatchsame-sex", "Pr(>|t|)"],3))
It is estimated that compared to the mixed-sex pairs, the same-sex pairs would have approximately r abs(round(discord_cat_mean[["coefficients"]][["SEX_binarymatchsame-sex"]],3)) higher S00_H40_mean. However, this coefficient is not significant, so it is not advisable to interpret the coefficient.
Multi-Match Coding for Sex
discord_cat_mean2 <- lm(S00_H40_mean ~ SEX_multimatch, data = cat_sex )
discord_cat_mean2 %>% # for nicer regression output broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
There is a significant difference between female-female pairs and male-male pairs (r round(summary(discord_cat_mean2)[["coefficients"]]["SEX_multimatchMALE", "Pr(>|t|)"],3)) to predict the S00_H40_mean. However, there is no significant difference between mixed-sex pairs and female-female pairs (p = r round(summary(discord_cat_mean2)[["coefficients"]]["SEX_multimatchmixed", "Pr(>|t|)"],3)).
The coefficient r abs(round(discord_cat_mean2[["coefficients"]]["SEX_multimatchMALE"],3)) is the difference between the expected S00_H40_mean (the mean SES score for the siblings) for the reference group (in this case, the female-female pairs) and the male-male pairs. It can be concluded that male-male pairs and female-female pair has significant differences in S00_H40_mean.
The coefficient r abs(round(discord_cat_mean2[["coefficients"]]["SEX_multimatchmixed"],3)) is the difference between the expected S00_H40_mean for the reference group (in this case, the female-female pairs) and the mixed-sex pairs. However, these coefficients are not significant, so it is not advisable to interpret the coefficients.
Regression Analysis: Race Variables
For race variables, we use the multi-match coding to examine differences between minority and non-minority pairs:
Multimatch
The regression model with a multi-match race variable as a predictor can be conducted as such:
# perform kinship regressions cat_race_reg <- discord_regression( data = df_link, outcome = "S00_H40", sex = "SEX", race = "RACE", demographics = "race", predictors = NULL, pair_identifiers = c("_S1", "_S2"), coding_method = "multi" )
cat_race_reg %>% # for nicer regression output broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The mean SES score for the siblings (S00_H40_mean) is a significant control variable (p =r round(summary(cat_race_reg)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3). The term S00_H40_mean is negatively associated with the difference score of SES between siblings (S00_H40_diff), controlling for another variable (in this case, RACE_multimatchNONMINORITY). It is estimated that for one unit increase of S00_H40_mean, the DV (S00_H40_diff) is expected to decrease by approximately
r abs(round(cat_race_reg[["coefficients"]][["S00_H40_mean"]],3)).
The term RACE_multimatchNONMINORITY was a significant predictor of S00_H40_diff (p = r round(summary(cat_race_reg)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)) after controlling for S00_H40_mean. This means that the difference between the "Minority-minority" sibling pairs and "nonminority-non-minority" sibling pairs significantly predicts S00_H40_diff. Specifically, compared to the reference group (the "minority" pairs), "nonminority" pairs are expected to have approximately r abs(round(cat_race_reg[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) lower S00_H40_diff.
Mean SES Model with Race
We can also examine whether race composition predicts mean SES levels:
discord_cat_mean <- lm(S00_H40_mean ~ RACE_multimatch, data = cat_race )
discord_cat_mean %>% # for nicer regression output broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
There is significant difference between "minority" pairs and "nonminority" pairs in S00_H40_mean (p =r round(summary(discord_cat_mean)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)).
It is estimated that, compared to the reference group (minority pairs), the nonminority pairs would have approximately
r abs(round(discord_cat_mean[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) lower S00_H40_mean.
Regression Analysis: Combined Sex and Race Variables
We can include both sex and race as predictors in the same model:
Like before we restructure the data for the kinship-discordant regression, but this time we using the discord_regression() function, which calls the discord_data() function internally.
Multimatch
both_multi <- discord_regression( data = df_link, outcome = "S00_H40", sex = "SEX", race = "RACE", demographics = "both", predictors = NULL, pair_identifiers = c("_S1", "_S2"), coding_method = "multi" )
both_multi %>% # for nicer regression output broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation
The mean SES score for the siblings (S00_H40_mean) is a significant control variable (p = r round(summary(both_multi)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3) ). S00_H40_mean is negatively associated with the difference score of SES between the siblings (S00_H40_diff), controlling for other variables (in this case, the SEX_multimatchMALE, SEX_multimatchmixed and RACE_multimatchNONMINORITY). It is estimated that for one unit increase of the mean SES score for the sibling pairs( S00_H40_mean), the difference score of SES between siblings(S00_H40_diff) is expected to decrease approximately r round(both_multi[["coefficients"]][["S00_H40_mean"]],3).
The SEX_multimatchmixed and SEX_multimatchMALE are not significant predictors when controlling for other variables (i.e., S00_H40_mean and RACE_multimatchNONMINORITY). The coefficient r round(both_multi[["coefficients"]][["SEX_multimatchMALE"]],3) is the difference between the expected DV (S00_H40_diff) for the reference group (in this case, the "female-female" pairs) and the "male-male" pairs. The coefficient r round(both_multi[["coefficients"]][["SEX_multimatchmixed"]],3) is the difference between the expected DV (S00_H40_diff) for the female-female pairs and the mixed-sex pairs. However, these coefficients are not significant, so it is not advisable to interpret the coefficients.
The term RACE_multimatchNONMINORITY is a significant predictor (p = r round(summary(both_multi)[["coefficients"]]["RACE_multimatchNONMINORITY", "Pr(>|t|)"],3)) when controlling for other variables (i.e., SEX_multimatchMALE, SEX_multimatchmixed, and S00_H40_mean). This means that there is a significant difference between minority race pairs and nonminority race pairs in the difference score of SES between siblings (S00_H40_diff) when controlling for the model covariates (i.e., SEX_multimatchMALE, SEX_multimatchmixed, and S00_H40_mean). Specifically, compared to the minority race pairs, the nonminority race pairs were expected to have approximately r round(both_multi[["coefficients"]][["RACE_multimatchNONMINORITY"]],3) higher difference score of SES between siblings at age 40.
Alternative Model: Binary Sex Match and Multi-Match Race
To combine binary and multi-match coding approaches, we can use the standard lm() function:
We can perform regression using the binary-match sex variable and multi-match race variable as such:
discord_cat_diff <- lm( S00_H40_diff ~ S00_H40_mean + RACE_multimatch + SEX_binarymatch, data = cat_both )
# for nicer regression output discord_cat_diff %>% broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The mean SES score for the siblings at 40 (S00_H40_mean) is a significant control variable (p =
r round(summary(discord_cat_diff)[["coefficients"]]["S00_H40_mean","Pr(>|t|)"],3). The mean SES score for the siblings (S00_H40_mean) is negatively associated with the difference score of SES between the siblings (S00_H40_diff), controlling for other variables (in this case, SEX_binarymatchsame-sex and RACE_multimatchNONMINORITY). It is estimated that for one unit increase of S00_H40_mean, the DV (S00_H40_diff) is expected to decrease approximately r abs(round(discord_cat_diff[["coefficients"]][["S00_H40_mean"]],3)).
The term SEX_binarymatchsame-sex is not a significant predictor (p = r round(summary(discord_cat_diff)[["coefficients"]][["SEX_binarymatchsame-sex", "Pr(>|t|)"]],3)) when controlling for other variables (i.e., S00_H40_mean and RACE_multimatchNONMINORITY). This means that the difference between same-sex pairs and mixed-sex pairs does not significantly predict the difference score of SES between siblings (S00_H40_diff) when controlling for the mean SES score for the siblings (S00_H40_mean) and race-composition of the pair (RACE_multimatchNONMINORITY). Compared to the mixed-sex pairs, it is estimated that the same-sex pairs have approximately r abs(round(discord_cat_diff[["coefficients"]][["SEX_binarymatchsame-sex"]],3))higher difference score of SES between siblings (S00_H40_diff) when controlling for the mean SES score for the sibling pairs (S00_H40_mean) and race-composition of the pairs (RACE_multimatchNONMINORITY). However, this coefficient is not statistically significant and should not be interpreted.
The term RACE_multimatchNONMINORITYis a significant predictor (p = r round(summary(discord_cat_diff)[["coefficients"]][["RACE_multimatchNONMINORITY", "Pr(>|t|)"]],3)). This means that there is a significant difference between minority race pairs and nonminority race pairs to predict the difference score of SES between the siblings (S00_H40_diff) when controlling for the model covariates (i.e., SEX_binarymatchsame-sex and S00_H40_mean). Specifically, compared to the minority race pairs, nonminority race pairs were expected to have approximately r abs(round(discord_cat_diff[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) lower difference scores of SES between siblings (S00_H40_diff).
Mean SES Models with Both Variables
Finally, we examine how sex and race together predict mean SES levels:
discord_cat_mean <- lm( S00_H40_mean ~ RACE_multimatch + SEX_multimatch, data = cat_both )
discord_cat_mean %>% broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The term SEX_multimatchMALE is a significant predictor (p = r round(summary(discord_cat_mean)[["coefficients"]]["SEX_multimatchMALE","Pr(>|t|)"],3)) when controlling for other variables (i.e., SEX_multimatchmixedand RACEe_multimatchNONMINORITY). This means that the difference between female-female pairs and male-male pairs significantly predicted the mean SES score for the siblings when controlling for race-composition of the pairs. Compared to the female-female pairs, it is estimated that the male-male pairs have approximately
r abs(round(discord_cat_mean[["coefficients"]][["SEX_multimatchMALE"]],3)) higher mean SES score for the siblings when controlling for and race-composition of the pairs.
The term SEX_multimatchmixed was not a significant predictor (p = r round(summary(discord_cat_mean)[["coefficients"]]["SEX_multimatchmixed","Pr(>|t|)"],3)) when controlling for other variables (i.e., SEX_multimatchMALEand RACE_multimatchNONMINORITY). This means that the difference between female-female pairs and mixed-sex pairs does not significantly predict the mean SES score for the siblings when controlling for race-composition of the pairs. Compared to the female-female pairs, it is estimated that the mixed-sex pairs have approximately
r abs(round(discord_cat_mean[["coefficients"]][["SEX_multimatchmixed"]],3)) higher mean SES score for the sibling pairs when controlling for and race-composition of the pairs. However, this variable is not significant, so it is not advisable to interpret the coefficient.
The term RACE_multimatchNONMINORITY is a significant predictor (p = r round(summary(discord_cat_mean)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)). This means that there is a significant difference between minority race pairs and nonminority race pairs in the mean SES score for the sibling pairs (S00_H40_mean) when controlling for the other variables (i.e., SEX_multimatchmixed and SEX_multimatchMALE). Specifically, compared to the minority race pairs, nonminority race pairs were expected to have approximately r abs(round(discord_cat_mean[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) higher mean SES score for siblings
Mean SES Models with Combining multimatch and binarymatch
discord_cat_mean2 <- lm(S00_H40_mean ~ RACE_multimatch + SEX_binarymatch, data = cat_both )
discord_cat_mean2 %>% broom::tidy() %>% mutate( p.value = scales::pvalue(p.value, add_p = TRUE), across(.cols = where(is.numeric), ~ round(.x, 3)) ) %>% rename( "Standard Error" = std.error, "T Statistic" = statistic ) %>% rename_with(~ snakecase::to_title_case(.x)) %>% kableExtra::kbl("html", align = "c") %>% kableExtra::kable_styling() %>% kableExtra::column_spec(1:5, extra_css = "text-align: center;")
Interpretation:
The term SEX_binarymatchsame-sex is not a significant predictor (p = r round(summary(discord_cat_mean2)[["coefficients"]]["SEX_binarymatchsame-sex","Pr(>|t|)"],3)) when controlling for the race-composition variable (i.e., RACE_multimatchNONMINORITY). This means that the difference between mixed-sex pairs and same sex pairs does not significantly predict the mean SES score for the siblings when controlling for race-composition of the pairs. Compared to the mixed-sex pairs, it is estimated that the same-sex pairs have approximately
r abs(round(discord_cat_mean2[["coefficients"]][["SEX_binarymatchsame-sex"]],3)) higher mean SES score for the sibling pairs (S00_H40_mean) when controlling for and race-composition of the pairs (RACE_multimatchNONMINORITY). However, this variable is not significant, so it is not advisable to interpret the coefficient.
The term RACE_multimatchNONMINORITY is a significant predictor (p = r round(summary(discord_cat_mean2)[["coefficients"]]["RACE_multimatchNONMINORITY","Pr(>|t|)"],3)). This means that there is a significant difference between minority race pairs and nonminority race pairs in the the mean SES score for the siblings when controlling for the sex-composition variable (i.e., SEX_binarymatchsame-sex). Specifically, compared to the minority race pairs, nonminority race pairs were expected to have approximately r abs(round(discord_cat_mean2[["coefficients"]][["RACE_multimatchNONMINORITY"]],3)) higher mean SES score for siblings
Conclusion
This vignette has demonstrated how to incorporate categorical predictors in discordant-kinship regression analyses using the discord package.
Key findings and recommendations include:
- Variable Type Matters: Categorical variables must be handled differently depending on whether they are between-dyads variables (like race in our filtered sample) or mixed variables (like sex in sibling pairs).
- Coding Approaches Offer Different Insights:
- Binary match coding examines whether similarity/difference matters
- Multi-match coding allows for more detailed examination of specific category effects
Implementation Recommendations:
For implementation in your own research, we recommend:
- Consider the theoretical nature of your categorical predictors
- Use discord_data() to prepare categorical variables appropriately
- Choose coding schemes based on your specific research questions
- Carefully interpret results in light of variable coding decisions
References
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