Fitting the ACE(t)-p model

Description

The ACE(t)-p model with the A, C and E variance components as functions with respect to age modelled by P-splines.

Usage

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AtCtEtp(data_m, data_d, knot_a = 8, knot_c = 8, knot_e = 8, eps = 0.1, 
mod=c('d','d','d'), robust = 0)

Arguments

data_m

An N_m x 3 data matrix for MZ twins. N_m is the number of MZ twin pairs. The first two columns are centered trait values (i.e. the mean should be zero) and the third column is age (or other covariates).

data_d

An N_d x 3 data matrix for DZ twins. N_d is the number of DZ twin pairs. The first two columns are centered trait values (i.e. the mean should be zero) and the third column is age (or other covariates).

knot_a

The number of interior knots of the B-spline for the A component. The default value is 8.

knot_c

The number of interior knots of the B-spline for the C component. The default value is 8.

knot_e

The number of interior knots of the B-spline for the E component. The default value is 8.

eps

Tolerance for convergence of the EM algorithm iterations. The default value is 0.1.

mod

A character vector of length 3. Each element specifies the function for the A, C or E component respectively. The components can be 'd'(dynamic), 'c'(constant) or 'l'(linear). The default is c('d','d','d').

robust

An integer indicating the number of different initial values that the function will randomly generate and try in the optimization. The default value is 0.

Details

When the 'mod' argument for a component is 'd'(dynamic), the corresponding 'beta' is the spline coefficients. When the 'mod' argument for a component is 'l'(linear), the corresponding 'beta' is a vector of two values, the exponential of which (exp(beta)) are the variances at the minimum and maximum age (or other covariates) provided in the data. When the 'mod' argument for a component is 'c'(constant), the corresponding 'beta' has only one value and exp(beta) is the variance.

Value

var_b_a

The estimated variance for the penalized coefficient for the A components.

var_b_c

The estimated variance for the penalized coefficient for the C components.

var_b_e

The estimated variance for the penalized coefficient for the E components.

beta_a

The estimated spline coefficients of the A component. See 'details' for more information.

beta_c

The estimated spline coefficients of the C component. See 'details' for more information.

beta_e

The estimated spline coefficients of the E component. See 'details' for more information.

con

An indicator of convergence of the optimization algorithm. An integer code 0 indicates successful completion. See 'optim' for more details.

lik

The minus log marginal likelihood.

knot_a

A vector of the knot positions for the A component.

knot_c

A vector of the knot positions for the C component.

knot_e

A vector of the knot positions for the E component.

Author(s)

Liang He

References

He, L., Sillanpää, M.J., Silventoinen, K., Kaprio, J. and Pitkäniemi, J., 2016. Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models. Genetics, 202(4), pp.1313-1328.

Examples

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# data(data_ace)

# result <- AtCtEtp(data_ace$mz, data_ace$dz, knot_e = 7, knot_c = 5, mod=c('d','d','d'))