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.
Japanese help file: (smn_JPH)

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 = \sum_{i} f_i \log{p(x_i)}
where
p(x_i) = c \times dnorm( x_i, mu, sigma )
and c = 1 / \sum_{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 )

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