Handling categorical predictors with discord

Introduction

Purpose

This vignette demonstrates how to incorporate categorical predictors into discordant-kinship regression analyses using the discord package. Building on dyadic modeling strategies from Kenny et al. (Kenny, Kashy, and Cook 2006) and extensions to kinship models in our prior work (Hwang 2022), 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 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 are constant within dyads.
- Example: For full siblings, race is often a between-dyad variable.
Within-dyad variables vary within dyads but remain constant across dyads (rare for categorical variables).
- Example: Division of chores between roommates (must sum to 100%).
Mixed variables can 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. For categorical variables, these operations are not meaningful (Kenny, Kashy, and Cook 2006). Use coding strategies designed for categories instead.

Coding Approaches for Categorical Variables

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

Binary-match coding collapses all category pairings into a single indicator showing whether two members of a dyad share the same category (1) or differ (0).
Multi-match coding preserves information about which category the pair matches on. So rather than coding all same-category pairs identically, it distinguishes, for example, male–male from female–female pairings.

Binary-match Coding

Binary match coding creates a simple indicator of whether pairs match (1) or differ (0) on a single 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 preserves the identity of the specific category shared within each pair, allowing distinctions among same-category matches:

Male-male pairs → “MALE”
Female-female pairs → “FEMALE”
Mixed pairs → “MIXED”

Use case: when the goal is to compare category-specific effects (for example, male-male versus female-female pairs) rather than simply testing for similarity or difference.

As noted by Hwang and Garrison (Hwang 2022), the appropriate coding strategy should follow the conceptual level of your research question and the theoretical justification for distinguishing categories.

Data Preparation

To illustrate these coding approaches, we use sibling data from the 1979 National Longitudinal Survey of Youth (NLSY79). The example begins by loading the required packages and preparing an analysis dataset that links siblings, filters relevant variables, and recodes categorical predictors.

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)

Next, we filter and clean the NLSY79 data, construct kinship links, and recode the categorical variables. In this example, we restrict to 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 NlsyLinkspackage to merge the kinship linkage data with the target variables. The resulting dataset is structured in wide format, with suffixes identifying the two siblings within 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 siblings, we remove cases with missing values. Sex and race are recoded as factors to prepare them for analysis.

# 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"
    )
  )

Because race is typically constant within families of full siblings, it functions as a between-dyad variable. For illustration purposes, we restrict the analytic sample 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()

Here, slice_sample() randomly selects one pair per household. In practice, researchers may choose to select the oldest or youngest pair instead by using slice_min() or slice_max().

Handling Categorical Predictors

Mixed Variables: Sex as an Example

Sex is a mixed variable in sibling studies because it can vary within some pairs and also across pairs. Families may include same-sex or mixed-sex sibling pairs, and that 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:

id	S00_H40_1	S00_H40_2	S00_H40_diff	S00_H40_mean	SEX_1	SEX_2	SEX_binarymatch	SEX_multimatch
359	80.83837	46.83232	34.006052	63.83535	FEMALE	FEMALE	same-sex	FEMALE
363	79.39371	74.43080	4.962906	76.91225	FEMALE	MALE	mixed-sex	mixed
492	70.61552	50.76235	19.853172	60.68894	FEMALE	MALE	mixed-sex	mixed
85	48.54822	35.09636	13.451863	41.82229	FEMALE	FEMALE	same-sex	FEMALE
131	49.05986	35.82118	13.238680	42.44052	MALE	FEMALE	mixed-sex	mixed
299	47.78226	31.52980	16.252455	39.65603	MALE	MALE	same-sex	MALE

The dataset contains the following sex pairings:

SEX_1	SEX_2	sample_size
FEMALE	FEMALE	416
FEMALE	MALE	358
MALE	FEMALE	429
MALE	MALE	396

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:

binary	multi	SEX_1	SEX_2	sample_size
mixed-sex	mixed	FEMALE	MALE	358
mixed-sex	mixed	MALE	FEMALE	429
same-sex	FEMALE	FEMALE	FEMALE	416
same-sex	MALE	MALE	MALE	396

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 table below reports the race composition of pairs.

RACE_binarymatch	RACE_multimatch	RACE_1	RACE_2	sample_size
same-race	MINORITY	MINORITY	MINORITY	778
same-race	NONMINORITY	NONMINORITY	NONMINORITY	821

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 different-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 different-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 different-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 ~ "diff-race",
      RACE_binarymatch == 1 ~ "same-race"
    ),
    SEX_binarymatch = case_when(
      SEX_binarymatch == 0 ~ "mixed-sex",
      SEX_binarymatch == 1 ~ "same-sex"
    )
  )

RACE_multi	RACE_1	RACE_2	SEX_binary	SEX_multi	SEX_1	SEX_2	sample_size
MINORITY	MINORITY	MINORITY	mixed-sex	mixed	FEMALE	MALE	179
MINORITY	MINORITY	MINORITY	mixed-sex	mixed	MALE	FEMALE	201
MINORITY	MINORITY	MINORITY	same-sex	FEMALE	FEMALE	FEMALE	204
MINORITY	MINORITY	MINORITY	same-sex	MALE	MALE	MALE	194
NONMINORITY	NONMINORITY	NONMINORITY	mixed-sex	mixed	FEMALE	MALE	179
NONMINORITY	NONMINORITY	NONMINORITY	mixed-sex	mixed	MALE	FEMALE	228
NONMINORITY	NONMINORITY	NONMINORITY	same-sex	FEMALE	FEMALE	FEMALE	212
NONMINORITY	NONMINORITY	NONMINORITY	same-sex	MALE	MALE	MALE	202

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"
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	23.952	1.166	20.534	p<0.001
S00_H40_mean	-0.090	0.020	-4.561	p<0.001
SEX_binarymatch	0.024	0.750	0.031	p=0.975

Interpretation:

We predict sibling differences in SES (S00_H40_diff).

The mean SES score (S00_H40_mean) is a significant control variable (p =0). 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 -0.09.
The binary sex match variable SEX_binarymatch is not a significant predictor (p = 0.975), 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"
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	24.523	1.248	19.647	p<0.001
S00_H40_mean	-0.075	0.020	-3.673	p<0.001
SEX_multimatchMALE	-0.380	1.053	-0.361	p=0.718
SEX_multimatchmixed	-0.192	0.907	-0.212	p=0.832
RACE_multimatchNONMINORITY	-2.277	0.772	-2.950	p=0.003

Interpretation:

The term S00_H40_mean was a significant control variable (p = 0). 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 0.075.
There was no significant difference between female-female pairs and male-male pairs (p=0.718) to predict S00_H40_diff. Similarly, there were no significant differences between mixed-sex pairs and female-female pairs (p = 0.832).
The coefficient 0.38 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 0.192 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
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	52.399	0.675	77.576	p<0.001
SEX_binarymatchsame-sex	0.018	0.948	0.019	p=0.985

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=0.985)

It is estimated that compared to the mixed-sex pairs, the same-sex pairs would have approximately 0.018 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
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	50.529	0.927	54.516	p<0.001
SEX_multimatchMALE	3.872	1.327	2.917	p=0.004
SEX_multimatchmixed	1.870	1.146	1.632	p=0.103

Interpretation:

There is a significant difference between female-female pairs and male-male pairs (0.004) to predict the S00_H40_mean. However, there is no significant difference between mixed-sex pairs and female-female pairs (p = 0.103).

The coefficient 3.872 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 1.87 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"
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	24.361	1.108	21.987	p<0.001
S00_H40_mean	-0.076	0.020	-3.712	p<0.001
RACE_multimatchNONMINORITY	-2.272	0.771	-2.945	p=0.003

Interpretation:

The mean SES score for the siblings (S00_H40_mean) is a significant control variable (p =0. 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 0.076.

The term RACE_multimatchNONMINORITY was a significant predictor of S00_H40_diff (p = 0.003) 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 2.272 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
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	47.645	0.659	72.335	p<0.001
RACE_multimatchNONMINORITY	9.277	0.919	10.092	p<0.001

Interpretation:

There is significant difference between “minority” pairs and “nonminority” pairs in S00_H40_mean (p =0). It is estimated that, compared to the reference group (minority pairs), the nonminority pairs would have approximately 9.277 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"
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	24.523	1.248	19.647	p<0.001
S00_H40_mean	-0.075	0.020	-3.673	p<0.001
SEX_multimatchMALE	-0.380	1.053	-0.361	p=0.718
SEX_multimatchmixed	-0.192	0.907	-0.212	p=0.832
RACE_multimatchNONMINORITY	-2.277	0.772	-2.950	p=0.003

Interpretation

The mean SES score for the siblings (S00_H40_mean) is a significant control variable (p = 0 ). 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 -0.075.

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 -0.38 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 -0.192 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 = 0.003) 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 -2.277 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
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	24.357	1.172	20.787	p<0.001
S00_H40_mean	-0.076	0.020	-3.711	p<0.001
RACE_multimatchNONMINORITY	-2.272	0.771	-2.944	p=0.003
SEX_binarymatchsame-sex	0.007	0.748	0.009	p=0.993

Interpretation:

The mean SES score for the siblings at 40 (S00_H40_mean) is a significant control variable (p = 0. 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 0.076.

The term SEX_binarymatchsame-sex is not a significant predictor (p = 0.993) 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 0.007higher 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 = 0.003). 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 2.272 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
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	45.801	1.013	45.210	p<0.001
RACE_multimatchNONMINORITY	9.277	0.917	10.114	p<0.001
SEX_multimatchMALE	3.867	1.287	3.005	p=0.003
SEX_multimatchmixed	1.800	1.111	1.620	p=0.105

Interpretation:

The term SEX_multimatchMALE is a significant predictor (p = 0.003) 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 3.867 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 = 0.105) 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 1.8 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 = 0). 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 9.277 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
)

Term	Estimate	Standard Error	T Statistic	P Value
(Intercept)	47.601	0.809	58.803	p<0.001
RACE_multimatchNONMINORITY	9.278	0.920	10.090	p<0.001
SEX_binarymatchsame-sex	0.086	0.919	0.093	p=0.926

Interpretation:

The term SEX_binarymatchsame-sex is not a significant predictor (p = 0.926) 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 0.086 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 = 0). 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 9.278 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

Hwang, Yoo Ri. 2022. “Dueling Dyads: Regression Versus MLM Analysis with a Categorical Predictor.” Master's thesis, Wake Forest University.

Kenny, David A., Deborah A. Kashy, and William L. Cook. 2006. Dyadic Data Analysis. Dyadic Data Analysis. New York, NY, US: Guilford Press.

Yoo Ri Hwang and S. Mason Garrison

Introduction

Purpose

Understanding Variable Types in Dyadic Analysis

Coding Approaches for Categorical Variables

Binary-match Coding

Multi-match Coding

Data Preparation

Package Loading and Data Setup

Handling Categorical Predictors

Mixed Variables: Sex as an Example

Between-dyad Variable: Race as an Example

Combining Binary and Multi-match Variables

Results and Interpretation

Regression Analysis: Sex Variables

Binary Match Coding for Sex

Interpretation:

Multi-Match Coding for Sex

Interpretation:

Mean SES Model with Sex

Interpretation:

Multi-Match Coding for Sex

Interpretation:

Regression Analysis: Race Variables

Multimatch

Interpretation:

Mean SES Model with Race

Interpretation:

Regression Analysis: Combined Sex and Race Variables

Multimatch

Interpretation

Alternative Model: Binary Sex Match and Multi-Match Race

Interpretation:

Mean SES Models with Both Variables

Interpretation:

Mean SES Models with Combining multimatch and binarymatch

Interpretation:

Conclusion

Implementation Recommendations:

References