walsFit: Fitter function for Weighted Average Least Squares estimation
In WALS: Weighted-Average Least Squares Model Averaging

walsFit

R Documentation

Fitter function for Weighted Average Least Squares estimation

Description

Workhorse function behind wals and walsGLM.

Usage

walsFit(
  X1,
  X2,
  y,
  sigma = NULL,
  prior = weibull(),
  method = "original",
  svdTol = .Machine$double.eps,
  svdRtol = 1e-06,
  keepUn = FALSE,
  eigenSVD = TRUE,
  prescale = TRUE,
  postmult = FALSE,
  ...
)

Arguments

`X1`	Design matrix for focus regressors. Usually includes a constant (column full of 1s) and can be generated using `model.matrix`.
`X2`	Design matrix for auxiliary regressors. Usually does not include a constant column and can also be generated using `model.matrix`.
`y`	Response as vector.
`sigma`	if NULL (default), then the variance of the error term is estimated, see p.136 of \insertCitemagnus2016wals;textualWALS. If sigma is specified, then the unrestricted estimator is divided by sigma before performing the Bayesian posterior mean estimation.
`prior`	Object of class `"familyPrior"`. For example `weibull` or `laplace`.
`method`	Specifies method used. Available methods are `"original"` (default) or `"svd"`.
`svdTol`	Tolerance for rank of matrix `\bar{Z}_{1}` Only used if `method = "svd"`. Checks if smallest eigenvalue in SVD of `\bar{Z}_1` and `\bar{Z}` is larger than `svdTol`, otherwise reports a rank deficiency.
`svdRtol`	Relative tolerance for rank of matrix `\bar{Z}_{1}`. Only used if `method = "svd"`. Checks if ratio of largest to smallest eigenvalue in SVD of `\bar{Z}_1` is larger than `svdRtol`, otherwise reports a rank deficiency.
`keepUn`	If `TRUE`, keeps the estimators of the unrestricted model, i.e. `\tilde{\gamma}_{u}`.
`eigenSVD`	If `TRUE`, then `semiorthogonalize` uses `svd` to compute the eigendecomposition of `\bar{\Xi}` instead of `eigen`. In this case, the tolerances of `svdTol` and `svdRtol` are used to determine whether `\bar{\Xi}` is of full rank (need it for `\bar{\Xi}^{-1/2}`).
`prescale`	If `TRUE` (default), prescales the regressors X1 and X2 with `\Delta_1` and `\Delta_2`, respectively, to improve numerical stability and make the coefficients of the auxiliary regressors scale equivariant. See \insertCitedeluca2011stata;textualWALS for more details. WARNING: It is not recommended to set `prescale = FALSE`. The option `prescale = FALSE` only exists for historical reasons.
`postmult`	If `TRUE`, then it computes `Z_{2} = X_{2} \Delta_{2} T \Lambda^{-1/2} T^{\top},` where `T` contains the eigenvectors and `\Lambda` the eigenvalues from the eigenvalue decomposition `\Xi = \Delta_2 X_{2}^{\top} M_{1} X_{2} \Delta_2 = T \Lambda T^{\top},` instead of `Z_{2} = X_{2} \Delta_{2} T \Lambda^{-1/2}.` See \insertCitehuynhwals;textualWALS for more details. The latter is used in the original MATLAB code for WALS in the linear regression model \insertCitemagnus2010growth,deluca2011stata,kumar2013normallocation,magnus2016walsWALS, see eq. (12) of \insertCitemagnus2016wals;textualWALS. The first form is required in eq. (9) of \insertCitedeluca2018glm;textualWALS. It is not recommended to set `postmult = FALSE` when using `walsGLM` and `walsNB`.
`...`	Arguments for internal function `computePosterior`.

Value

A list containing

`coef`	Model averaged estimates of all coefficients.
`beta1`	Model averaged estimates of the coefficients of the focus regressors.
`beta2`	Model averaged estimates of the coefficients of the auxiliary regressors.
`gamma1`	Model averaged estimates of the coefficients of the transformed focus regressors.
`gamma2`	Model averaged estimates of the coefficients of the transformed auxiliary regressors.
`vcovBeta`	Estimated covariance matrix of the regression coefficients.
`vcovGamma`	Estimated covariance matrix of the coefficients of the transformed regressors.
`sigma`	Estimated or prespecified standard deviation of the error term.
`prior`	`familyPrior`. The `prior` specified in the arguments.
`method`	Stores `method` used from the arguments.
`betaUn1`	If `keepUn = TRUE`, contains the unrestricted estimators of the coefficients of the focus regressors.
`betaUn2`	If `keepUn = TRUE`, contains the unrestricted estimators of the coefficients of the auxiliary regressors.
`gammaUn1`	If `keepUn = TRUE`, contains the unrestricted estimators of the coefficients of the transformed focus regressors.
`gammaUn2`	If `keepUn = TRUE`, contains the unrestricted estimators of the coefficients of the transformed auxiliary regressors.
`fitted.values`	Estimated conditional means of the data.
`residuals`	Residuals, i.e. response - fitted mean.
`X1names`	Names of the focus regressors.
`X2names`	Names of the auxiliary regressors.
`k1`	Number of focus regressors.
`k2`	Number of auxiliary regressors.
`n`	Number of observations.
`condition`	Condition number of the matrix `\Xi = \Delta_{2} X_{2}^{\top} M_{1} X_{2} \Delta_{2}`.

References

\insertAllCited

Examples

X <- model.matrix(gdpgrowth ~ lgdp60 + equipinv + school60 + life60 + popgrowth
                  + law + tropics + avelf + confucian, data = GrowthMPP)
X1 <- X[, c("(Intercept)", "lgdp60", "equipinv", "school60", "life60", "popgrowth")]
X2 <- X[, c("law", "tropics", "avelf", "confucian")]
y <- GrowthMPP$gdpgrowth

walsFit(X1, X2, y, prior = weibull(), method = "svd")

WALS documentation built on June 22, 2024, 9:42 a.m.