bayz: Bayesian mixed linear and shrinkage models

In MarniTausen/BayzR: R package for bayz

Bayesian mixed linear and shrinkage models

Description

The bayz function fits various mixed-linear and Bayesian shrinkage models with complex covariance structures using an extended R-formula syntax.

Usage

bayz(model, data = NULL, chain = c(0, 0, 0), silent = FALSE, ...)

Arguments

model	A formula describing the model to be fit.
data	Data frame to collect data from
chain	Vector describing the number of iterations to be run.
silent	Boolean to switch on/off printing to R console
...	Additional parameters passed onto the Model function.

Details

The model formula in bayz has the basic syntax of an R formula but with all explanatory (right-hand-side) terms wrapped by a function to specify how to fit the explanatory variables in the model. This may look like Yield ~ fx(Year) + rn(Variety) to fit Yield with Year as a fixed factor and Variety as a random factor. The equivalent lme4 model would be Yield ~ factor(Year) + (1|Variety). The list of model functions currently available is: fx() (fixed factors), rn() (random factors), rg() (fixed regressions), and rr() (random regressions). The model functions allow to specify interactions of variables, hierarchies, use of matrices as input data, complex covariance structures, and prior distributions can be changed to modify standard mixed model in Bayesian shrinkage models.

Interactions between fators are specified using the colon, for instance by writing for a fixed Year-Location interaction fx(Year:Location). Bayz does NOT support automatic expansion with main effects by using the 'star' (Year*Location) or 'forward slash' (Year/Location) syntaxes, hence bayz requires to manually add the desired main effects in the model (but note that bayz uses the 'forward slash' to specify hierarchical models). Interactions between factors can be specified to any degree. The 'star' syntax can be used to indicate interaction between covariates, like rg(TempSum*Precip), where it is simply interpreted as multiplication. Interaction between a covariate and a factor is specified using the 'pipe' character as in lme4 models. It can be used to specify fixed nested regressions as rg(TempSum|Year:Location) to specify regressions on TempSum within each Year-Location, or to speficy random slope models in rr(), for instance rr(TempSum|Variety).

The bayz call has a data argument to specify an input data-frame (the "main data") to contain model variables, but bayz will also search the R environment if variables are not found in the main data. Typically, input in the form of matrices such as large sets of covariates, proportional variance-covariance / correlation / kernel / similarity matrices used in variance models, as well as data for hierarchical models, are not in the main data. Matrices / kernels should be prepared with row-names to match a variable in the data. For matrices / kernels used in variance models, the link is straightforward, for instance in rn(Variety:Location, V=KG*KE), KG and KE can be a genetic and environmental kinship / kernel matrix, respectively, and KG should have row-names matching Variety levels, while KE should have row-names matching Location levels. To fit a large set of covariates, the match is specified using a hierachical specification rr(Variety/Metabolites), where Metabolites is then a matrix of covariates which must have row-names matching Variety levels. In both cases, such kernel or covariate matrices must have unique levels, but the main data may have repeated levels and in different order. If one has repeated metabolite data on each Variety, for instance at multiple time-points, then consider that Variety is not the appropriate link to the data, but Variety:Time is.

For random effects a variance-covariance structure can be specified using a V= option within the model-term function, for example rn(Variety, V=KG). When the fit is for an interaction of factors, the variance specification should expand to include one term for each variable, separated by stars (which should be read as Kronecker products). The variance structure is then built up from a combination of given (proportional) variance-covariance / correlation / kernel matrices and predefined acronyms IDEN, DIAG and VCOV that indicate parameterized matrices (with parameters to be estimated from the data). Alternatively, the variance structure can be specified as a linear model using V=~, which is interpreted as a use of a log-linear model for the variances.

Value

A fitted bayz model

MarniTausen/BayzR documentation built on April 4, 2024, 9:30 a.m.