The function mc_mixed helps to build the components
of the matrix linear predictor associated with mixed models. It is
useful to model the covariance structure as a function of known
covariates in a linear mixed model fashion (Bonat, et. al. 2016).
The mc_mixed function was designed to analyse repeated measures
and longitudinal data, where in general the observations are taken
at a fixed number of groups, subjects or unit samples.
mc_mixed(formula, data)
| formula | a formula model to build the matrix linear predictor. See details. |
|---|---|
| data | data set. |
Bonat, W. H. (2018). Multiple Response Variables Regression Models in R: The mcglm Package. Journal of Statistical Software, 84(4):1--30.
Bonat, et. al. (2016). Modelling the covariance structure in marginal multivariate count models: Hunting in Bioko Island. Journal of Agricultural Biological and Environmental Statistics, 22(4):446--464.
A list of matrices.
The formula argument should be specified similar to
the linear predictor for the mean structure, however the first
component should be 0 and the second component should always
indicate the name of the column containing the subject
or unit sample index. It should be a factor. The other covariates
are specified after a slash "\" in the usual way. For example,
~0 + SUBJECT/(x1 + x2) means that the column SUBJECT contains the
subject or unit sample index, while the covariates that can be continuous
or factors are given in the columns x1 and x2. Be careful the parenthesis
after the "\" are mandatory, when including more than one covariate.
The special case where only the SUBJECT effect is requested the formula
takes the form ~ 0 + SUBJECT without any extra covariate.
This structure corresponds to the well known compound symmetry structure.
By default the function mc_mixed include all interaction terms,
the users can ignore the interactions terms removing them from the
matrix linear predictor.
mc_id, mc_conditional_test,
mc_dist, mc_ma, mc_rw and mc_car.
SUBJECT <- gl(2, 6) x1 <- rep(1:6, 2) x2 <- rep(gl(2,3),2) data <- data.frame(SUBJECT, x1 , x2) # Compound symmetry structure mc_mixed(~0 + SUBJECT, data = data)#> [[1]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 1 1 1 1 1 1 . . . . . . #> 2 1 1 1 1 1 1 . . . . . . #> 3 1 1 1 1 1 1 . . . . . . #> 4 1 1 1 1 1 1 . . . . . . #> 5 1 1 1 1 1 1 . . . . . . #> 6 1 1 1 1 1 1 . . . . . . #> 7 . . . . . . 1 1 1 1 1 1 #> 8 . . . . . . 1 1 1 1 1 1 #> 9 . . . . . . 1 1 1 1 1 1 #> 10 . . . . . . 1 1 1 1 1 1 #> 11 . . . . . . 1 1 1 1 1 1 #> 12 . . . . . . 1 1 1 1 1 1 #># Compound symmetry + random slope for x1 and interaction or correlation mc_mixed(~0 + SUBJECT/x1, data = data)#> [[1]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 1 1 1 1 1 1 . . . . . . #> 2 1 1 1 1 1 1 . . . . . . #> 3 1 1 1 1 1 1 . . . . . . #> 4 1 1 1 1 1 1 . . . . . . #> 5 1 1 1 1 1 1 . . . . . . #> 6 1 1 1 1 1 1 . . . . . . #> 7 . . . . . . 1 1 1 1 1 1 #> 8 . . . . . . 1 1 1 1 1 1 #> 9 . . . . . . 1 1 1 1 1 1 #> 10 . . . . . . 1 1 1 1 1 1 #> 11 . . . . . . 1 1 1 1 1 1 #> 12 . . . . . . 1 1 1 1 1 1 #> #> [[2]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 1 2 3 4 5 6 . . . . . . #> 2 2 4 6 8 10 12 . . . . . . #> 3 3 6 9 12 15 18 . . . . . . #> 4 4 8 12 16 20 24 . . . . . . #> 5 5 10 15 20 25 30 . . . . . . #> 6 6 12 18 24 30 36 . . . . . . #> 7 . . . . . . 1 2 3 4 5 6 #> 8 . . . . . . 2 4 6 8 10 12 #> 9 . . . . . . 3 6 9 12 15 18 #> 10 . . . . . . 4 8 12 16 20 24 #> 11 . . . . . . 5 10 15 20 25 30 #> 12 . . . . . . 6 12 18 24 30 36 #> #> [[3]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 2 3 4 5 6 7 . . . . . . #> 2 3 4 5 6 7 8 . . . . . . #> 3 4 5 6 7 8 9 . . . . . . #> 4 5 6 7 8 9 10 . . . . . . #> 5 6 7 8 9 10 11 . . . . . . #> 6 7 8 9 10 11 12 . . . . . . #> 7 . . . . . . 2 3 4 5 6 7 #> 8 . . . . . . 3 4 5 6 7 8 #> 9 . . . . . . 4 5 6 7 8 9 #> 10 . . . . . . 5 6 7 8 9 10 #> 11 . . . . . . 6 7 8 9 10 11 #> 12 . . . . . . 7 8 9 10 11 12 #># Compound symmetry + random slope for x1 and x2 plus interactions mc_mixed(~0 + SUBJECT/(x1 + x2), data = data)#> [[1]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 1 1 1 1 1 1 . . . . . . #> 2 1 1 1 1 1 1 . . . . . . #> 3 1 1 1 1 1 1 . . . . . . #> 4 1 1 1 1 1 1 . . . . . . #> 5 1 1 1 1 1 1 . . . . . . #> 6 1 1 1 1 1 1 . . . . . . #> 7 . . . . . . 1 1 1 1 1 1 #> 8 . . . . . . 1 1 1 1 1 1 #> 9 . . . . . . 1 1 1 1 1 1 #> 10 . . . . . . 1 1 1 1 1 1 #> 11 . . . . . . 1 1 1 1 1 1 #> 12 . . . . . . 1 1 1 1 1 1 #> #> [[2]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 1 2 3 4 5 6 . . . . . . #> 2 2 4 6 8 10 12 . . . . . . #> 3 3 6 9 12 15 18 . . . . . . #> 4 4 8 12 16 20 24 . . . . . . #> 5 5 10 15 20 25 30 . . . . . . #> 6 6 12 18 24 30 36 . . . . . . #> 7 . . . . . . 1 2 3 4 5 6 #> 8 . . . . . . 2 4 6 8 10 12 #> 9 . . . . . . 3 6 9 12 15 18 #> 10 . . . . . . 4 8 12 16 20 24 #> 11 . . . . . . 5 10 15 20 25 30 #> 12 . . . . . . 6 12 18 24 30 36 #> #> [[3]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 . . . . . . . . . . . . #> 2 . . . . . . . . . . . . #> 3 . . . . . . . . . . . . #> 4 . . . 1 1 1 . . . . . . #> 5 . . . 1 1 1 . . . . . . #> 6 . . . 1 1 1 . . . . . . #> 7 . . . . . . . . . . . . #> 8 . . . . . . . . . . . . #> 9 . . . . . . . . . . . . #> 10 . . . . . . . . . 1 1 1 #> 11 . . . . . . . . . 1 1 1 #> 12 . . . . . . . . . 1 1 1 #> #> [[4]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 2 3 4 5 6 7 . . . . . . #> 2 3 4 5 6 7 8 . . . . . . #> 3 4 5 6 7 8 9 . . . . . . #> 4 5 6 7 8 9 10 . . . . . . #> 5 6 7 8 9 10 11 . . . . . . #> 6 7 8 9 10 11 12 . . . . . . #> 7 . . . . . . 2 3 4 5 6 7 #> 8 . . . . . . 3 4 5 6 7 8 #> 9 . . . . . . 4 5 6 7 8 9 #> 10 . . . . . . 5 6 7 8 9 10 #> 11 . . . . . . 6 7 8 9 10 11 #> 12 . . . . . . 7 8 9 10 11 12 #> #> [[5]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 . . . 1 1 1 . . . . . . #> 2 . . . 1 1 1 . . . . . . #> 3 . . . 1 1 1 . . . . . . #> 4 1 1 1 2 2 2 . . . . . . #> 5 1 1 1 2 2 2 . . . . . . #> 6 1 1 1 2 2 2 . . . . . . #> 7 . . . . . . . . . 1 1 1 #> 8 . . . . . . . . . 1 1 1 #> 9 . . . . . . . . . 1 1 1 #> 10 . . . . . . 1 1 1 2 2 2 #> 11 . . . . . . 1 1 1 2 2 2 #> 12 . . . . . . 1 1 1 2 2 2 #> #> [[6]] #> 12 x 12 sparse Matrix of class "dsCMatrix"#>#> #> 1 . . . 1 1 1 . . . . . . #> 2 . . . 2 2 2 . . . . . . #> 3 . . . 3 3 3 . . . . . . #> 4 1 2 3 8 9 10 . . . . . . #> 5 1 2 3 9 10 11 . . . . . . #> 6 1 2 3 10 11 12 . . . . . . #> 7 . . . . . . . . . 1 1 1 #> 8 . . . . . . . . . 2 2 2 #> 9 . . . . . . . . . 3 3 3 #> 10 . . . . . . 1 2 3 8 9 10 #> 11 . . . . . . 1 2 3 9 10 11 #> 12 . . . . . . 1 2 3 10 11 12 #>