$\beta\in \R^{d}$ is the vector of regression coefficients and $b\in\R$ is the intercept.
Popular examples of link functions are the logit link function where for any real $z$,
$g(z)=e^z/(1+e^z)$ and the probit link function where $g(z)=\Phi(z),$ with $\Phi$
-the cumulative distribution function of the standard normal ${\cal N}(0,1)$.
+the cumulative distribution function of the standard normal ${\mathcal N}(0,1)$.
Both are implemented in the package.
If now we want to modelise heterogeneous populations, let $K$ be the number of
populations and $\omega=(\omega_1,\cdots,\omega_K)$ their weights such that
-$\omega_{j}\geq 0$, $j=1,\ldots,K$ and $\sum_{j=1}^{K}\omega{j}=1$.
+$\omega_{j}\geq 0$, $j=1,\ldots,K$ and $\sum_{j=1}^{K}\omega_{j}=1$.
Define, for $j=1,\ldots,K$, the regression coefficients in the $j$-th population
by $\beta_{j}\in\R^{d}$ and the intercept in the $j$-th population by
$b_{j}\in\R$. Let $\omega =(\omega_{1},\ldots,\omega_{K})$,
symetric $d\times d$ matrix. ***** TODO: take this into account? -->
The two main functions are:
+
* computeMu(), which estimates the parameters directions, and
* optimParams(), which builds an object \code{o} to estimate all other parameters
when calling \code{o$run()}, starting from the directions obtained by the
previous function.
+
A third function is useful to run Monte-Carlo or bootstrap estimations using
different models in various contexts: multiRun(). We'll show example for all of them.
The following function builds and return an optimization algorithm object:
```{r, results="show", include=TRUE, echo=TRUE}
-M <- computeMoments(io$X, io$Y)
-# X and Y must be provided if the moments matrix is not given
-algopt <- optimParams(K=2, link="probit", optargs=list(M=M))
+# M <- computeMoments(io$X, io$Y) #optional (if several runs)
+algopt <- optimParams(io$X, io$Y, K=2, link="probit") #, M=M)
# Optimization starts at beta = mu, b = 0 and p = uniform distribution
x0 <- list(beta = mu)
theta <- algopt$run(x0)
```{r, results="show", include=TRUE, echo=TRUE}
# Second row, first column; morpheus on the left, flexmix on the right
-plotBox(mr1, 2, 1, "Target value: -1")
+plotBox(mr1, 2, 1, main="Target value: -1")
```
```{r, results="show", include=TRUE, echo=TRUE}
function(fargs) {
library(morpheus)
mu <- computeMu(fargs$X, fargs$Y, fargs$optargs)
- optimParams(fargs$K,fargs$link,fargs$optargs)$run(list(beta=mu))$beta
+ optimParams(fargs$X,fargs$Y,fargs$K,fargs$link,fargs$M)$run(list(beta=mu))$beta
},
# flexmix
function(fargs) {
fargs$Y = io$Y
fargs$K = ncol(fargs$beta)
fargs$link = fargs$optargs$link
- fargs$optargs$M = computeMoments(io$X,io$Y)
+ fargs$M = computeMoments(io$X,io$Y)
fargs
}, N=10, ncores=3)
# As in example 1, align results:
```{r, results="show", include=TRUE, echo=TRUE}
# Second argument = true parameters matrix; third arg = index of method (here "morpheus")
-plotCoefs(mr2, beta, 1)
+plotCoefs(mr2[[1]], beta, 1)
+plotCoefs(mr2[[2]], beta, 1)
# Real params are on the continous line; estimations = dotted line
```
projects / morpheus.git / commitdiff