| Title: | Multivariate Mixed Effects Model |
| Version: | 0.1.1 |
| Depends: | R (≥ 3.3.0) |
| Maintainer: | Luyao Peng <luyaopeng.cn@gmail.com> |
| Description: | Analyzing data under multivariate mixed effects model using multivariate REML and multivariate Henderson3 methods. See Meyer (1985) <doi:10.2307/2530651> and Wesolowska Janczarek (1984) <doi:10.1002/bimj.4710260613>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| Imports: | stats, MASS, Matrix, jointDiag, lme4, matrixcalc, psych, stringr |
| BugReports: | https://github.com/pengluyaoyao/MMeM/issues |
| NeedsCompilation: | no |
| Packaged: | 2021-09-07 15:16:34 UTC; pengluyao |
| Author: | Luyao Peng [aut, cre], Rui Yang [aut] |
| Repository: | CRAN |
| Date/Publication: | 2021-09-08 08:00:14 UTC |
MMeM: Estimating the variance covariance components of the multivariate mixed effects model
Description
This package analyzes data under multivariate mixed effects model using multivariate REML and multivariate Henderson3 methods. Currently, it only supports multivariate mixed effects model with one fixed effects and one random effects and two response variates. See Meyer (1985) <doi:10.2307/2530651> and Wesolowska Janczarek (1984) <doi:10.1002/bimj.4710260613>.
Author(s)
Luyao Peng luyaopeng.cn@gmail.com
Rui Yang ray.cn.us@gmail.com
See Also
Useful links:
Report bugs at https://github.com/pengluyaoyao/MMeM/issues
Multivariate Henderson3 method
Description
Multivariate Henderson3 method
Usage
MMeM_henderson3(fml, data, factor_X)
Arguments
fml |
two-sided linear formula object describing both the fixed-effects and random-effects parts of the model, with the response on the left of a ~ operator. For univariate response, put variable name directly; for multivariate responses combine variables using concatenate operator, for example, for bivariate responses, c(var1, var2). The predictor terms are separated by + operators, on the right. Random-effects terms are distinguished by vertical bars '|' separating expressions for design matrices from grouping factors. |
data |
data frame containing the variables named in formula. |
factor_X |
(logical) indicating whether predictor is a factor or continuous. By default is TRUE |
Value
The function returns a list with the following objects:
-
T.estimatesis the estimated variance covariance components (T.estimates) of the variance covariance matrix of the block random effects with corresponding sampling variances (T.variance) -
E.estimatesis the estimated variance covariance components (E.estimates) of the variance covariance matrix of the residuals with corresponding sampling variances (E.variance)
References
Wesolowska Janczarek, M. T. "Estimation of covariance matrices in unbalanced random and mixed multivariate models." Biometrical journal 26.6 (1984): 665,674.
Examples
data(simdata)
results_henderson <- MMeM_henderson3(fml = c(V1,V2) ~ X_vec + (1|Z_vec),
data = simdata, factor_X = TRUE)
Multivariate REML Method
Description
Estimating the variance components under the multivariate mixed effects model using REML methods
Usage
MMeM_reml(fml, data, factor_X, T.start, E.start, maxit = 50,
tol = 1e-09)
Arguments
fml |
a two-sided linear formula object describing both the fixed-effects and random-effects parts of the model, with the response on the left of a ~ operator. For univariate response, put variable name directly; for multivariate responses combine variables using concatenate operator, for example, for bivariate responses, c(var1, var2). The predictor terms are separated by + operators, on the right. Random-effects terms are distinguished by vertical bars '|' separating expressions for design matrices from grouping factors. |
data |
data frame containing the variables named in formula. |
factor_X |
(logical) indicating whether predictor is a factor or continuous. By default is TRUE |
T.start |
the starting matrix for the variance covariance matrix of the block random effects, it has to be positive definite q by q symmetric matrix. |
E.start |
the starting matrix for the variance covariance matrix of the block random effects, it has to be positive definite q by q symmetric matrix. |
maxit |
the maximum number of iterations |
tol |
the convergence tolerance |
Details
Suppose n observational units, q variates, p fixed effects coefficients and s random effects units. The model supports multivariate mixed effects model for one-way randomized block design with equal design matrices:
Y = XB + ZU + E
where Y is n by q response variates matrix; X is n by p design matrix for the fixed effects; B is p by q coefficients matrix for the fixed effects; Z is n by s design matrix for the random effects; U is s by q matrix for the random effects; E is n by q random errors matrix.
The model also supports simple OLS multivariate regression:
y = Xb + Zu + e
where y is n by 1 response vector; b is p by 1 coefficients vector for the fixed effects; u is s by 1 matrix for the random effects.
Value
The function returns a list with the following objects:
-
T.estimatesis the estimated variance covariance components of the variance covariance matrix of the block random effects -
E.estimatesis the estimated variance covariance components of the variance covariance matrix of the residuals -
VCOVis the asymptotic dispersion matrix of the estimated variance covariance components for the block random effects and the residuals.
References
Meyer, K. "Maximum likelihood estimation of variance components for a multivariate mixed model with equal design matrices." Biometrics 1985: 153,165.
Examples
data(simdata)
T.start <- matrix(c(10,5,5,15),2,2)
E.start <- matrix(c(10,1,1,3),2,2)
results_reml <- MMeM_reml(fml = c(V1,V2) ~ X_vec + (1|Z_vec), data = simdata,
factor_X = TRUE, T.start = T.start, E.start = E.start, maxit = 10)
parses formulas to creates model matrices
Description
parses formulas to creates model matrices
Usage
MMeM_terms(fml, data, factor_X)
Arguments
fml |
a two-sided linear formula object describing both the fixed-effects and random-effects parts of the model, with the response on the left of a ~ operator. For univariate response, put variable name directly; for multivariate responses combine variables using concatenate operator, for example, for bivariate responses, c(var1, var2). The predictor terms are separated by + operators, on the right. Random-effects terms are distinguished by vertical bars '|' separating expressions for design matrices from grouping factors. |
data |
data frame containing the variables named in formula. |
factor_X |
(logical) indicating whether predictor is a factor or continuous. By default is TRUE |
simulated bivariate data
Description
This is a simulated data with 2 dependent variables and one fixed effects and one random effects
Usage
data(simdata)
Details
simulated datasets