ACDE: Fit AE, ACE or ADE biometric mixed models to nuclear family...

In gap: Genetic Analysis Package

Fit AE, ACE or ADE biometric mixed models to nuclear family data

Description

Fits classical biometric variance–decomposition models using a linear mixed model formulation implemented with nlme::lme.

Usage

ACDE(model, data, type = c("AE", "ACE", "ADE"), method = "ML")

Arguments

model	Fixed-effects formula.
data	Data frame in long format (one row per individual).
type	Model type: "AE", "ACE" or "ADE".
method	Estimation method: "ML" (default) or "REML".

Details

The function estimates additive genetic (A), shared environmental (C), dominance genetic (D), and unique environmental (E) variance components from nuclear family data (parents and offspring) in long format.

Supported family structures:

• Parent-child trios (one offspring)

• Nuclear families with any number of siblings

The function automatically detects the family structure and selects the correct additive-genetic parameterisation.

Only AE, ACE and ADE models are fitted.

Phenotypic variance is decomposed as

V_P = V_A + V_C + V_D + V_E

The model is fitted as a linear mixed model with family-level random effects and individual residual variance.

Automatic family detection

The function detects whether families contain one or multiple offspring.

• Trios: collapsed additive parameterisation.

• Siblings: transmission decomposition parameterisation.

Trio parameterisation

Additive effects represented as:

A = 0.5 Mother + 0.5 Father + 1 Child

This reproduces the expected parent–offspring covariance:

Cov = 1/2 V_A

Multi-sibling parameterisation

Additive genetic variance is decomposed into:

• maternal transmission (A_m)

• paternal transmission (A_f)

• Mendelian sampling (M_s)

For offspring:

A = A_m + A_f + M_s

Total additive variance:

V_A = 2(\sigma^2_{Am} + \sigma^2_{Af}) + \sigma^2_{Ms}

This produces correct covariances:

• Parent–offspring: 1/2 V_A

• Sibling–sibling: 1/2 V_A

This formulation generalises to any number of siblings.

Identifiability of C and D

Nuclear family data cannot fully separate shared environment (C) and dominance (D). ACE and ADE models should be interpreted jointly.

Value

Object of class "ACDEfit" containing:

• fit nlme::lme object

• var Variance components (A,C,D,E)

• h2 Narrow-sense heritability

• c2 Shared environment (ACE only)

• d2 Dominance (ADE only)

• H2 Broad-sense heritability (ADE only)

Required columns in data

• familyid Nuclear family identifier.

• var1 Maternal transmission coefficient.

• var2 Paternal transmission coefficient.

• var3 Offspring (Mendelian sampling) indicator.

These variables encode expected genetic transmission and are not role indicators.

Coding for a nuclear family:

role     var1  var2  var3
-------------------------
father     0     1     0
mother     1     0     0
child      1     1     1

For multiple siblings, each offspring receives identical coding:

role     var1  var2  var3
-------------------------
father     0     1     0
mother     1     0     0
sib1       1     1     1
sib2       1     1     1
sib3       1     1     1

Note

This complements pbsize() and fbsize().

Author(s)

ChatGPT

Examples

library(nlme)
set.seed(1)

simulate_families <- function(n_fam = 200)
{
  VA <- 0.4; VC <- 0.2; VD <- 0.1; VE <- 0.3
  out <- list()

  for(f in 1:n_fam){
    Cfam <- rnorm(1,0,sqrt(VC))
    Af <- rnorm(1,0,sqrt(VA))
    Am <- rnorm(1,0,sqrt(VA))

    make_child <- function(){
      Mend <- rnorm(1,0,sqrt(0.5*VA))
      A  <- 0.5*(Af+Am)+Mend
      D  <- rnorm(1,0,sqrt(VD))
      E  <- rnorm(1,0,sqrt(VE))
      A + D + Cfam + E
    }

    out[[f]] <- data.frame(
      familyid=f,
      role=c("father","mother","sib1","sib2","sib3"),
      y=c(
        Af + Cfam + rnorm(1,0,sqrt(VE)),
        Am + Cfam + rnorm(1,0,sqrt(VE)),
        make_child(), make_child(), make_child()
      )
    )
  }

  dat <- do.call(rbind,out)

  dat$var1 <- as.integer(dat$role=="mother")
  dat$var2 <- as.integer(dat$role=="father")
  dat$var3 <- as.integer(grepl("sib", dat$role))
  dat
}

dat <- simulate_families()

AE  <- ACDE(y~1, dat, "AE")
ACE <- ACDE(y~1, dat, "ACE")
ADE <- ACDE(y~1, dat, "ADE")

anova(AE$fit, ACE$fit, ADE$fit)

############################################################
# Create rectangular variance table (important!)
############################################################

summary(AE)
summary(ACE)
summary(ADE)

require(gap.datasets)
model <- bwt ~ male + first + midage + highage + birthyr
AE <- ACDE(model,mfblong)
ACE <- ACDE(model,mfblong,type="ACE")
ADE <- ACDE(model,mfblong,type="ADE")
anova(AE$fit,ACE$fit,ADE$fit)

gap documentation built on May 28, 2026, 9:07 a.m.