# Factmle_cov: Calculates the Maximum likelihood Factor analysis with a... In FACTMLE: Maximum Likelihood Factor Analysis

## Description

Calculates the Maximum likelihood Factor analysis with a covariance Matrix.

## Usage

 ```1 2``` ```Factmle_cov(S, rnk, Psi_init = c(), lb = 0.01, index = c(), lb2 = 0.01, tol = 10^-7, Max_iter = 1000) ```

## Arguments

 `S` The Covariance Matrix. It is a p*p numeric matrix, where p is the number of variables. `rnk` Rank constraint for the Factor analysis problem. It must a positive integer less than the number of variables p `Psi_init` The initial value of Psi. It is a p*1 numeric vetor, where p is the number of variables.Default value is a vector of uniform random numbers. `lb` The lower bound on the Psi values. The default value is set to 0.05 `index` This option is for modified version of factmle.The default value is a null vector. If assigned a zero vector, it will perform MLFA keeping some of the Psi values specified by the index at a specifed level *lb2* `lb2` This option of modified version of factmle algorithm. The default value is 0.001. The Psi values specified by the *index* is kept constant at *lb2* while doing MLFA. `tol` Precision parameter. Default is 10^-7 `Max_iter` Maximum number of iterations. Default is 1000.

## Value

A list with the following components

Psi

A vector containing the unique variances.

Lambda

Nll

A vector containing the negative Log-likelihood values at every iteration.

Nllopt

The value of the negative log-likelihood upon convergence.

`eigs_sym`
 ```1 2 3 4 5 6 7``` ```library(MASS) library(stats) Psi=runif(15,min=0.2,max=1.3) Lambda=mvrnorm(n=15,mu=rep(0,3),Sigma = diag(rep(1,3))) data=mvrnorm(n=5000,mu=rep(0,15),Sigma = diag(Psi)+Lambda%*%t(Lambda)) S=cov(data) x=Factmle_cov(S,3) ```