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Demonstrating Categorical Predictors in Discordant-Kinship Regressions"

Demonstrating Categorical Predictors in Discordant-Kinship Regressions"
In discord: Functions for Discordant Kinship Modeling 

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. Drawing on dyadic modeling strategies described by Kenny et al. [@kenny2006] and their extension to kinship settings by Hwang and Garrison [@Hwang2022], we present a several approaches to handling categorical variables like sex and race in these specialized regression models.

We focus on:

  1. How to code and interpret categorical variables at different levels (between-dyads vs. mixed)
  2. Different methods for treating categorical predictors (binary match vs. multi match)
  3. Practical implementation using the discord package functions

To illustrate these concepts, we examine whether sex and race predict socioeconomic status (SES) at age 40, using different categorical coding schemes with 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:

We have summarized these variable types in the table 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 |

When analyzing continuous predictors, we typically calculate mean scores and difference scores. However, as Kenny et al. [@kenny2006] note, categorical variables require alternative approaches since mean and difference calculations aren't meaningful.

Coding Approaches for Categorical Variables

The discord package implements two primary coding strategies for categorical predictors:

  1. Binary Match Coding: Creates a binary indicator of whether pairs match (1) or differ (0) on the categorical variable.
  2. Multi-Match Coding: Preserves specific category information, allowing for more nuanced analysis.

Binary Match Coding

Binary match coding creates a simple indicator of whether pairs match (1) or differ (0) on the categorical variable: - Same-sex pairs (male-male or female-female) → 1 - Mixed-sex pairs (male-female) → 0

When to use: When your research question focuses on similarity versus difference rather than specific category effects.

Multi-Match Coding

Multi-match coding preserves specific category information: - Male-male pairs → "MALE" - Female-female pairs → "FEMALE" - Mixed pairs → "mixed"

When to use: When you hypothesize different effects for different categories (e.g., male pairs vs. female pairs).

Following Hwang and Garrison [@Hwang2022], the approach you select should align with your specific research questions and theoretical framework.

Data Preparation

We'll demonstrate categorical predictor handling using sibling data from the NLSY79. We first load necessary packages and prepare our 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 begin by filtering and cleaning the dataset, creating kinship links, and recoding categorical variables. In this example, we use 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)

Next, 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, with suffixes distinguishing the two individuals in each pair.

df_link <- CreatePairLinksSingleEntered(
  outcomeDataset = data_flu_ses,
  linksPairDataset = link_pairs,
  outcomeNames = link_vars
)

To ensure that the dependent variable (SES at age 40) is available for both members of the pair, we filter out missing values. We also recode sex and race into string labels and retain only same-race pairs to make race a between-dyads variable.

# 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"
    )
  )

# we only include same-race pairs in this example for demonstration purpose
df_link <- df_link %>%
  dplyr::filter(RACE_S1 == RACE_S2)

To avoid violating independence assumptions, we retain only one sibling pair per household:

df_link <- df_link %>%
  group_by(ExtendedID) %>%
  slice_sample() %>%
  ungroup()

Handling Categorical Predictors

@ Mixed Variables: Gender 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 can be of the same or different sexes, and the pattern 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 possible sex combinations in the dataset are:

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 above, the discord_data() function generates SEX_binarymatch and SEX_multimatch for the sex variable. By doing so, the sex variable (which was initially a mixed variable) becomes a between-dyad variable as follows:

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 based on their research question:

Between-dyad variable: Race as an Example

For demonstration purposes, we've already filtered our dataset to include only same-race pairs, making race a between-dyads variable. Let's prepare the data specifically for race analysis:

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:

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)

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. Because the race variable is a between-dyads variable, all the pairs in this example are same-race pairs. The RACE_multimatch variable indicates whether the pair is minority-minority, nonminority-nonminority, or mixed-race.

Combining Sex and Race Variables

We can also prepare data that includes both sex and race composition 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 combined race and sex compositions in the dataset are:

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)

Results and Interpretation

Regression Analysis: Sex Variables

Binary Match Coding for Sex

First, we examine whether same-sex versus mixed-sex pairs differ in SES discordance:

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:

Multi-Match Coding for Sex

Next, we test whether male-male, female-female, and mixed-sex pairs differ. 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:

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:

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:

First, we restructure the data for the kinship-discordant regression using the discord_data() function.

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 variable is not significant, so it is not advisable to interpret the coefficient.

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:

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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discord documentation built on April 12, 2025, 1:12 a.m.

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