The symbols used in the help pages and vignettes of VetResearchLMM, with their meaning and the argument or result component that holds them. The notation follows one rule throughout: scalars are upper-case letters in normal face (\(P\), \(R\)), indices lower-case italic (\(i, j\)), vectors lower-case bold (\(\mathbf{y}\), \(\boldsymbol{\beta}\)) and matrices upper-case bold (\(\mathbf{X}\), \(\boldsymbol{\Sigma}\)).
Usage
vlm_notation(format = c("table", "path", "tex"))See also
Other VetResearchLMM utilities:
autoplot.vlm_result(),
vlm_app(),
vlm_cite(),
vlm_interpret(),
vlm_reference(),
vlm_save(),
vlm_theme()
Author
Muhammad Yaseen (myaseen208@gmail.com)
Examples
vlm_notation(
format = "table"
)
#> symbol text kind
#> <char> <char> <char>
#> 1: N N scalar
#> 2: P P scalar
#> 3: \\mathbf{y} y vector
#> 4: \\mathbf{X} X matrix
#> 5: \\boldsymbol{\\beta} beta vector
#> 6: \\mathbf{Z} Z matrix
#> 7: \\mathbf{u} u vector
#> 8: \\mathbf{e} e vector
#> 9: \\mathbf{G} G matrix
#> 10: \\mathbf{R} R matrix
#> 11: \\mathbf{V} V matrix
#> 12: \\boldsymbol{\\theta} theta vector
#> 13: \\mathbf{V}_i V_i matrix
#> 14: \\mathbf{P} P matrix
#> 15: \\mathbf{C} C matrix
#> 16: \\ell_R, \\ell l function
#> 17: \\mathbf{l}, \\mathbf{L} L vector
#> 18: \\mathbf{k} k vector
#> 19: \\nu nu scalar
#> 20: \\mathbf{A} A matrix
#> 21: \\mathbf{\\Phi}_A Phi_A matrix
#> 22: \\sigma^2 sigma2 scalar
#> 23: \\sigma_k^2 sigma2_k scalar
#> 24: \\rho rho scalar
#> 25: \\mathrm{E}(MS) EMS function
#> 26: d d scalar
#> 27: s s scalar
#> symbol text kind
#> <char> <char> <char>
#> meaning
#> <char>
#> 1: number of observations
#> 2: rank of the fixed-effects design matrix
#> 3: response (observations)
#> 4: design matrix of the fixed effects (overparameterised: one column per level)
#> 5: fixed effects
#> 6: design matrix of the random effects
#> 7: random effects
#> 8: residual errors
#> 9: covariance matrix of the random effects
#> 10: covariance matrix of the residuals
#> 11: covariance matrix of the observations: Z G Z' + R
#> 12: covariance parameters (variance components, covariances, correlations)
#> 13: derivative of V with respect to the i-th covariance parameter
#> 14: V^-1 - V^-1 X (X' V^-1 X)^- X' V^-1
#> 15: (X' V^-1 X)^-: covariance matrix of the fixed-effects solution
#> 16: restricted and full log-likelihood
#> 17: coefficients of an estimate or contrast of fixed effects
#> 18: coefficients of random effects in a narrow-space estimate
#> 19: denominator degrees of freedom
#> 20: asymptotic covariance matrix of the covariance-parameter estimates
#> 21: Kenward-Roger adjusted covariance matrix of the fixed effects
#> 22: residual variance
#> 23: variance of the k-th random effect
#> 24: correlation of the first-order autoregressive or spatial power structure
#> 25: expected mean square
#> 26: number of covariance parameters
#> 27: number of subjects
#> meaning
#> <char>
#> argument
#> <char>
#> 1: data
#> 2: fixed
#> 3: fixed
#> 4: fixed
#> 5: fixed
#> 6: random
#> 7: random
#> 8:
#> 9: random
#> 10: repeated
#> 11:
#> 12:
#> 13:
#> 14:
#> 15:
#> 16: method
#> 17: L
#> 18: random
#> 19: ddfm
#> 20:
#> 21: ddfm
#> 22:
#> 23: random
#> 24: repeated
#> 25: type
#> 26:
#> 27: repeated
#> argument
#> <char>