smn {lazy.irt} R Documentation

## Parameter Estimation of Parametric (Normal pdf) Scored Multinomial Distributions

### Description

Maximum likelihood estimation of the parameters of the parametric (normal pdf) scored multinomial distribution.

### Usage

smn(
x,
f,
mu = NULL,
sigma = NULL,
estmu = 1,
estsigma = 1,
maxiter = 100,
eps = 1e-08,
print = 1,
plot = 0
)


### Arguments

 x Score (numerical category label) f Frequency vector which sums to unity mu Initial value of the mean paramter to be estimated or NULL sigma Initial value of sigma the sigma parameter to be estimated or NULL estmu = 0 to skip the estimation of mu estsigma = 0 to skip the estimation of sigma maxiter max # of iterations eps eps for convergence print = 1 to print result plot = 1 to plot result

### Details

Given data, (x,f), where x is the domain and f is the associated frequency,
this program maximizes the following multinomial log likelihood
lnL = ∑_{i} f_i \log{p(x_i)}
where
p(x_i) = c \times dnorm( x_i, mu, sigma )
and c = 1 / ∑_{i} dnorm( x_i, mu, sigma )
with respect to mu and sigma.

### Value

A list of:
P A vector of estimated probability
x A vector of score
mu Estimated mean parameter
sigma Estimated standard deviation parameter
estmu = 1 to estimate mu
estsigma = 1 to estimate sigma
llh Maximized log likelihood
mean Sample mean
std Sample standard deviation

### Examples

set.seed(1701)
n <- 1000
npoints <- 21
resg <- list(midpoints=c(-2,-1,0,1,2), freq=c(5,6,8,6,2))
res <- smn( resg$midpoints, resg$freq, print=1, plot=1, mu=0, sigma=1 )



[Package lazy.irt version 0.1.3 Index]