In jeksterslab/ramR: Reticular Action Model (RAM) Notation
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
Equations can be specified without explicitly showing the error terms.
The two-factor confirmatory factor analysis example in the Equations vignette
can be specified as follows.
eq <- "
# items
## loadings
eta[1] by y1 1
eta[1] by y2 lambda[y2]
eta[1] by y3 lambda[y3]
eta[2] by y4 1
eta[2] by y5 lambda[y5]
eta[2] by y6 lambda[y6]
## intercepts
y1 on 1 nu[y1]
y2 on 1 nu[y2]
y3 on 1 nu[y3]
y4 on 1 nu[y4]
y5 on 1 nu[y5]
y6 on 1 nu[y6]
# errors
## Symmetric - error variances
y1 with y1 theta[epsilon[1]]
y2 with y2 theta[epsilon[2]]
y3 with y3 theta[epsilon[3]]
y4 with y4 theta[epsilon[4]]
y5 with y5 theta[epsilon[5]]
y6 with y6 theta[epsilon[6]]
# factors
## variances and covariances
eta[1] with eta[1] psi[eta[11]]
eta[1] with eta[2] psi[eta[12]]
eta[2] with eta[2] psi[eta[22]]
## means
eta[1] on 1 0 # There is no need to define equations for parameters constrained to zero.
eta[2] on 1 0 # The following equations were added for completeness.
"
eq <- "
# items
## loadings
eta[1] by y1 1
eta[1] by y2 lambda[y2]
eta[1] by y3 lambda[y3]
eta[2] by y4 1
eta[2] by y5 lambda[y5]
eta[2] by y6 lambda[y6]
## intercepts
y1 on 1 nu[y1]
y2 on 1 nu[y2]
y3 on 1 nu[y3]
y4 on 1 nu[y4]
y5 on 1 nu[y5]
y6 on 1 nu[y6]
# errors
## Symmetric - error variances
y1 with y1 theta[epsilon[1]]
y2 with y2 theta[epsilon[2]]
y3 with y3 theta[epsilon[3]]
y4 with y4 theta[epsilon[4]]
y5 with y5 theta[epsilon[5]]
y6 with y6 theta[epsilon[6]]
# factors
## variances and covariances
eta[1] with eta[1] psi[eta[11]]
eta[1] with eta[2] psi[eta[12]]
eta[2] with eta[2] psi[eta[22]]
## means
eta[1] on 1 0 # There is no need to define equations for parameters constrained to zero.
eta[2] on 1 0 # The following equations were added for completeness.
"
knitr::include_graphics("figure2-1.png")
EqParse
The EqParse() function can parse the defined equation
and setup labels for the unknown parameters.
ramR::EqParse(eq)
Symbolic
Eq2RAM
The Eq2RAM() function constructs
the RAM notation matrix representation of the model.
It also updates the parameter table to include
RAM notation information.
RAM <- ramR::Eq2RAM(eq)
RAM$par.table
cat(
"\\begin{align*}",
"\\mathrm{variables}=",
yacR::as.tex(yacR::as.ysym.mat(RAM$variables)),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{A}=",
yacR::as.tex(RAM$A),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{S}=",
yacR::as.tex(RAM$S),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{u}=",
yacR::as.tex(RAM$u),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{F}=",
yacR::as.tex(RAM$Filter),
"\\end{align*}",
sep = ""
)
Eq2Expectations
The Eq2Expectations() function constructs the
mean and covariance expectations.
Expectations <- ramR::Eq2Expectations(eq)
The covariance expectations for all the variables
are given below.
latex <- ramR::Eq2Expectations(eq, format = "tex")
cat(
"\\begin{align*}",
"\\mathbf{C}=",
latex$C,
"\\end{align*}",
sep = ""
)
The scaled/standardized $\mathbf{C}$ matrix is given below.
$$r latex$C.scaled$$
The covariance expectations for the observed variables y1 to y6
are given below.
cat(
"\\begin{align*}",
"\\mathbf{M}=",
latex$M,
"\\end{align*}",
sep = ""
)
The scaled/standardized $\mathbf{M}$ matrix is given below.
$$r latex$M.scaled$$
The mean expectations for all the variables
are given below.
cat(
"\\begin{align*}",
"\\mathbf{v}=",
latex$v,
"\\end{align*}",
sep = ""
)
The mean expectations for the observed variables y1 to y6
are given below.
cat(
"\\begin{align*}",
"\\mathbf{g}=",
latex$g,
"\\end{align*}",
sep = ""
)
Scaled RAM Matrices
RAM.scaled <- ramR::RAMScaled(
A = yacR::as.ysym(RAM$A),
S = RAM$S,
Filter = RAM$Filter,
C = Expectations$C,
C.scaled = Expectations$C.scaled
)
$$
\mathbf{A}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$A.scaled)
$$
$$
\mathbf{S}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$S.scaled)
$$
Numerical
Values can be placed on the par.label column.
eq <- "
# items
## loadings
eta[1] by y1 1
eta[1] by y2 1
eta[1] by y3 1
eta[2] by y4 1
eta[2] by y5 1
eta[2] by y6 1
## intercepts
y1 on 1 0
y2 on 1 0
y3 on 1 0
y4 on 1 0
y5 on 1 0
y6 on 1 0
# errors
## Symmetric - error variances
y1 with y1 0.50
y2 with y2 0.50
y3 with y3 0.50
y4 with y4 0.50
y5 with y5 0.50
y6 with y6 0.50
# factors
## variances and covariances
eta[1] with eta[1] 1
eta[1] with eta[2] 0.50
eta[2] with eta[2] 1
## means
eta[1] on 1 0
eta[2] on 1 0
"
Eq2RAM
The Eq2RAM() function constructs
the RAM notation matrix representation of the model.
RAM <- ramR::Eq2RAM(eq)
cat(
"\\begin{align*}",
"\\mathrm{variables}=",
yacR::as.tex(yacR::as.ysym.mat(RAM$variables)),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{A}=",
yacR::as.tex(RAM$A),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{S}=",
yacR::as.tex(RAM$S),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{u}=",
yacR::as.tex(RAM$u),
"\\end{align*}",
sep = ""
)
cat(
"\\begin{align*}",
"\\mathbf{F}=",
yacR::as.tex(RAM$Filter),
"\\end{align*}",
sep = ""
)
Eq2Expectations
The Eq2Expectations() function constructs the
mean and covariance expectations.
Expectations <- ramR::Eq2Expectations(eq)
The covariance expectations for all the variables
are given below.
cat(
"\\begin{align*}",
"\\mathbf{C}=",
yacR::as.tex(Expectations$C),
"\\end{align*}",
sep = ""
)
The covariance expectations for the observed variables y1 to y6
are given below.
cat(
"\\begin{align*}",
"\\mathbf{M}=",
yacR::as.tex(Expectations$M),
"\\end{align*}",
sep = ""
)
The mean expectations for all the variables
are given below.
cat(
"\\begin{align*}",
"\\mathbf{v}=",
yacR::as.tex(Expectations$v),
"\\end{align*}",
sep = ""
)
The mean expectations for the observed variables y1 to y6
are given below.
cat(
"\\begin{align*}",
"\\mathbf{g}=",
yacR::as.tex(Expectations$g),
"\\end{align*}",
sep = ""
)
Scaled RAM Matrices
RAM.scaled <- ramR::RAMScaled(
A = RAM$A,
S = RAM$S,
Filter = RAM$Filter,
C = Expectations$C,
C.scaled = Expectations$C.scaled
)
$$
\mathbf{A}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$A.scaled)
$$
$$
\mathbf{S}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$S.scaled)
$$
Eq2Data
The Eq2Data() function simulates data
from the multivariate normal distribution.
Data <- ramR::Eq2Data(eq, n = 100000)
str(Data)
cov(Data)
colMeans(Data)
jeksterslab/ramR documentation built on March 14, 2021, 9:38 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
Equations can be specified without explicitly showing the error terms.
The two-factor confirmatory factor analysis example in the Equations vignette
can be specified as follows.
eq <- " # items ## loadings eta[1] by y1 1 eta[1] by y2 lambda[y2] eta[1] by y3 lambda[y3] eta[2] by y4 1 eta[2] by y5 lambda[y5] eta[2] by y6 lambda[y6] ## intercepts y1 on 1 nu[y1] y2 on 1 nu[y2] y3 on 1 nu[y3] y4 on 1 nu[y4] y5 on 1 nu[y5] y6 on 1 nu[y6] # errors ## Symmetric - error variances y1 with y1 theta[epsilon[1]] y2 with y2 theta[epsilon[2]] y3 with y3 theta[epsilon[3]] y4 with y4 theta[epsilon[4]] y5 with y5 theta[epsilon[5]] y6 with y6 theta[epsilon[6]] # factors ## variances and covariances eta[1] with eta[1] psi[eta[11]] eta[1] with eta[2] psi[eta[12]] eta[2] with eta[2] psi[eta[22]] ## means eta[1] on 1 0 # There is no need to define equations for parameters constrained to zero. eta[2] on 1 0 # The following equations were added for completeness. "
eq <- " # items ## loadings eta[1] by y1 1 eta[1] by y2 lambda[y2] eta[1] by y3 lambda[y3] eta[2] by y4 1 eta[2] by y5 lambda[y5] eta[2] by y6 lambda[y6] ## intercepts y1 on 1 nu[y1] y2 on 1 nu[y2] y3 on 1 nu[y3] y4 on 1 nu[y4] y5 on 1 nu[y5] y6 on 1 nu[y6] # errors ## Symmetric - error variances y1 with y1 theta[epsilon[1]] y2 with y2 theta[epsilon[2]] y3 with y3 theta[epsilon[3]] y4 with y4 theta[epsilon[4]] y5 with y5 theta[epsilon[5]] y6 with y6 theta[epsilon[6]] # factors ## variances and covariances eta[1] with eta[1] psi[eta[11]] eta[1] with eta[2] psi[eta[12]] eta[2] with eta[2] psi[eta[22]] ## means eta[1] on 1 0 # There is no need to define equations for parameters constrained to zero. eta[2] on 1 0 # The following equations were added for completeness. "
knitr::include_graphics("figure2-1.png")
EqParse
The EqParse() function can parse the defined equation
and setup labels for the unknown parameters.
ramR::EqParse(eq)
Symbolic
Eq2RAM
The Eq2RAM() function constructs
the RAM notation matrix representation of the model.
It also updates the parameter table to include
RAM notation information.
RAM <- ramR::Eq2RAM(eq)
RAM$par.table
cat( "\\begin{align*}", "\\mathrm{variables}=", yacR::as.tex(yacR::as.ysym.mat(RAM$variables)), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{A}=", yacR::as.tex(RAM$A), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{S}=", yacR::as.tex(RAM$S), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{u}=", yacR::as.tex(RAM$u), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{F}=", yacR::as.tex(RAM$Filter), "\\end{align*}", sep = "" )
Eq2Expectations
The Eq2Expectations() function constructs the
mean and covariance expectations.
Expectations <- ramR::Eq2Expectations(eq)
The covariance expectations for all the variables are given below.
latex <- ramR::Eq2Expectations(eq, format = "tex") cat( "\\begin{align*}", "\\mathbf{C}=", latex$C, "\\end{align*}", sep = "" )
The scaled/standardized $\mathbf{C}$ matrix is given below.
$$r latex$C.scaled$$
The covariance expectations for the observed variables y1 to y6
are given below.
cat( "\\begin{align*}", "\\mathbf{M}=", latex$M, "\\end{align*}", sep = "" )
The scaled/standardized $\mathbf{M}$ matrix is given below.
$$r latex$M.scaled$$
The mean expectations for all the variables are given below.
cat( "\\begin{align*}", "\\mathbf{v}=", latex$v, "\\end{align*}", sep = "" )
The mean expectations for the observed variables y1 to y6
are given below.
cat( "\\begin{align*}", "\\mathbf{g}=", latex$g, "\\end{align*}", sep = "" )
Scaled RAM Matrices
RAM.scaled <- ramR::RAMScaled( A = yacR::as.ysym(RAM$A), S = RAM$S, Filter = RAM$Filter, C = Expectations$C, C.scaled = Expectations$C.scaled )
$$
\mathbf{A}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$A.scaled)
$$
$$
\mathbf{S}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$S.scaled)
$$
Numerical
Values can be placed on the par.label column.
eq <- " # items ## loadings eta[1] by y1 1 eta[1] by y2 1 eta[1] by y3 1 eta[2] by y4 1 eta[2] by y5 1 eta[2] by y6 1 ## intercepts y1 on 1 0 y2 on 1 0 y3 on 1 0 y4 on 1 0 y5 on 1 0 y6 on 1 0 # errors ## Symmetric - error variances y1 with y1 0.50 y2 with y2 0.50 y3 with y3 0.50 y4 with y4 0.50 y5 with y5 0.50 y6 with y6 0.50 # factors ## variances and covariances eta[1] with eta[1] 1 eta[1] with eta[2] 0.50 eta[2] with eta[2] 1 ## means eta[1] on 1 0 eta[2] on 1 0 "
Eq2RAM
The Eq2RAM() function constructs
the RAM notation matrix representation of the model.
RAM <- ramR::Eq2RAM(eq)
cat( "\\begin{align*}", "\\mathrm{variables}=", yacR::as.tex(yacR::as.ysym.mat(RAM$variables)), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{A}=", yacR::as.tex(RAM$A), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{S}=", yacR::as.tex(RAM$S), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{u}=", yacR::as.tex(RAM$u), "\\end{align*}", sep = "" )
cat( "\\begin{align*}", "\\mathbf{F}=", yacR::as.tex(RAM$Filter), "\\end{align*}", sep = "" )
Eq2Expectations
The Eq2Expectations() function constructs the
mean and covariance expectations.
Expectations <- ramR::Eq2Expectations(eq)
The covariance expectations for all the variables are given below.
cat( "\\begin{align*}", "\\mathbf{C}=", yacR::as.tex(Expectations$C), "\\end{align*}", sep = "" )
The covariance expectations for the observed variables y1 to y6
are given below.
cat( "\\begin{align*}", "\\mathbf{M}=", yacR::as.tex(Expectations$M), "\\end{align*}", sep = "" )
The mean expectations for all the variables are given below.
cat( "\\begin{align*}", "\\mathbf{v}=", yacR::as.tex(Expectations$v), "\\end{align*}", sep = "" )
The mean expectations for the observed variables y1 to y6
are given below.
cat( "\\begin{align*}", "\\mathbf{g}=", yacR::as.tex(Expectations$g), "\\end{align*}", sep = "" )
Scaled RAM Matrices
RAM.scaled <- ramR::RAMScaled( A = RAM$A, S = RAM$S, Filter = RAM$Filter, C = Expectations$C, C.scaled = Expectations$C.scaled )
$$
\mathbf{A}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$A.scaled)
$$
$$
\mathbf{S}_{\mathrm{scaled}} = r yacR::as.tex(RAM.scaled$S.scaled)
$$
Eq2Data
The Eq2Data() function simulates data
from the multivariate normal distribution.
Data <- ramR::Eq2Data(eq, n = 100000) str(Data) cov(Data) colMeans(Data)
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