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# umxRun now detects raw RAM, and runs sat and ind. worth speeding this bit up a bit?
m3 <- mxModel("independence",
    # TODO: slightly inefficient, as this has an analytic solution
    mxMatrix(name = "variableLoadings" , type="Diag", nrow = nVar, ncol = nVar, free=T, values = independenceStarts), 
	# labels = loadingsLabels),
    mxAlgebra(name = "expCov", expression = variableLoadings %*% t(variableLoadings)),
    mxMatrix(name  = "expMean", type = "Full", nrow = 1, ncol = nVar, values = dataMeans, free = T, labels = meansLabels),
    mxFIMLObjective(covariance = "expCov", means = "expMean", dimnames = manifests),
    mxData(theData, type = "raw")
)

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# Things you should learn in school: Be able to answer any question of the form:
# "Which has more gravitational pull on a baby as it is born: the midwife, or the planet Jupiter?"

# baby ~ 5 kg
# Distance and mass of [Jupiter](http://en.wikipedia.org/wiki/Jupiter) 

gravitationalAttraction <- function(G = 6.674E-11, m1, m2, r){
  # G = 6.674E-11 # [Gravitational constant](http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation): N m^2 kg^-2
  G * (m1 * m2)/r^2
}

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# mixture distribution..
n = 100000;
distOne = rnorm(n,  50, 10)
distTwo = rnorm(n, 120, 15)
x = c(distOne,distTwo)
hist(x)
psych::kurtosi(x);psych::skew(x);

# DV <- sum of unobserved IVs
x = distOne + distTwo

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# Generate a 25-item test
nItems = 25
nOptions = 4
passCriterion = 3 # or better

correct_answers = sample(c(1:nOptions), nItems, replace = TRUE)
 
# ===================================
# = Generate 10000 random responses =
# ===================================

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# http://openmx.psyc.virginia.edu/getOpenMx.R
# run this as
# source_gist(11294078)
if (.Platform$OS.type == "windows") {
    if (!is.null(.Platform$r_arch) && .Platform$r_arch == "x64") {
        repos <- c('http://openmx.psyc.virginia.edu/packages/')
    } else {
        repos <- c('http://openmx.psyc.virginia.edu/32bit/')
    }
    install.packages(pkgs = c('OpenMx'), repos = repos)

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# http://openmx.psyc.virginia.edu/getOpenMxBeta.R

if(version$major < 3) {
	stop("We don't have beta for R 2.15 or below. Consider upgrading to R 3.1?\n
	You can get this from http://cran.r-project.org/")
}
if (.Platform$OS.type == "windows") {
    if (!is.null(.Platform$r_arch) && .Platform$r_arch == "x64") {
        repos <- c('http://openmx.psyc.virginia.edu/testing/')
    } else {

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message("load me with devtools::source_gist('11326436')")

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# R version 3.0.3 (2014-03-06) -- "Warm Puppy"
source("http://openmx.psyc.virginia.edu/getOpenMxBeta.R")
library("OpenMx")
packageVersion("OpenMx") # [1] ‘999.0.0.3473’

data(demoOneFactor)  

manifests <- names(demoOneFactor) 
latents   <- c("G")  
model <- mxModel(model="One Factor", type="RAM",

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library(OpenMx)
manifests = c("mpg", "disp", "gear")

# =============================
# = simple independence model =
# =============================
m1 <- mxModel("ind", type = "RAM",
	manifestVars = manifests,
	mxPath(from = manifests, arrows = 2),
	mxPath(from = "one", to = manifests),