nptestind: Nonparametric Test of Independence
In npsf: Nonparametric and Stochastic Efficiency and Productivity Analysis

Description Usage Arguments Details Value Note Author(s) References See Also Examples

In output based efficiency measurement, routine nptestind perform test that radial (Debreu-Farrell) output-based measure of technical efficiency under chosen assumption about the technology and mix of outputs are independent. In input-based efficiency measurement, routine nptestind perform test that radial (Debreu-Farrell) input-based measure of technical efficiency under chosen assumption about the technology and mix of inputs are independent. Testing is performed using bootstrap technique.

nptestind(formula, data, subset,
 rts = c("C", "NI", "V"), base = c("output", "input"),
 reps = 999, alpha = 0.05,
 print.level = 1, dots = TRUE)

`formula`	an object of class “formula” (or one that can be coerced to that class): a symbolic description of the model. The details of model specification are given under ‘Details’.
`data`	an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment (`formula`), typically the environment from which `teradial` is called.
`subset`	an optional vector specifying a subset of observations for which technical efficiency is to be computed.
`rts`	character or numeric. string: first letter of the word “c” for constant, “n” for non-increasing, or “v” for variable returns to scale assumption. numeric: 3 for constant, 2 for non-increasing, or 1 for variable returns to scale assumption.
`base`	character or numeric. string: first letter of the word “o” for computing output-based or “i” for computing input-based technical efficiency measure. string: 2 for computing output-based or 1 for computing input-based technical efficiency measure
`reps`	specifies the number of bootstrap replications to be performed. The default is 999. The minimum is 100. Adequate estimates of confidence intervals using bias-corrected methods typically require 1,000 or more replications.
`alpha`	sets significance level; default is `alpha=0.05`.
`dots`	logical. Relevant if `print.level>=1`. If TRUE, one dot character is displayed for each successful replication; if FALSE, display of the replication dots is suppressed.
`print.level`	numeric. 0 - nothing is printed; 1 - print summary of the model and data. 2 - print summary of technical efficiency measures. 3 - print estimation results observation by observation. Default is 1.

Testing is performed using bootstrap technique (see Wilson, 2003).

Results can be summarized using summary.npsf.

nptestrts returns a list of class npsf containing the following elements:

`K`	numeric: number of data points.
`M`	numeric: number of outputs.
`N`	numeric: number of inputs.
`rts`	string: RTS assumption.
`base`	string: base for efficiency measurement.
`reps`	numeric: number of bootstrap replications.
`alpha`	numeric: significance level.
`t4n`	numeric: value of the T4n statistic.
`pval`	numeric: p-value of the test of independence.

Results can be summarized using summary.npsf.

Oleg Badunenko <oleg.badunenko@brunel.ac.uk>

Färe, R. and Lovell, C. A. K. (1978), Measuring the technical efficiency of production, Journal of Economic Theory, 19, 150–162, doi: 10.1016/0022-0531(78)90060-1

Färe, R., Grosskopf, S. and Lovell, C. A. K. (1994), Production Frontiers, Cambridge U.K.: Cambridge University Press

Wilson P.W. (2003), Testing Independence in Models of Productive Efficiency, Journal of Productivity Analysis, 20, 361–390, doi: 10.1023/A:1027355917855

teradial, tenonradial, teradialbc, tenonradialbc, nptestrts, sf

## Not run: 

require( npsf )

# Prepare data and matrices

data( ccr81 )
head( ccr81 )

# Create some missing values

ccr81 [64, "x4"] <- NA # just to create missing
ccr81 [68, "y2"] <- NA # just to create missing

Y2 <- as.matrix( ccr81[ , c("y1", "y2", "y3"), drop = FALSE] )
X2 <- as.matrix( ccr81[ , c("x1", "x2", "x3", "x4", "x5"), drop = FALSE] )

# Perform nonparametric test that radial (Debreu-Farrell) 
# output-based measure of technical efficiency under assumption of 
# NIRS technology and mix of outputs are independent. Test is 
# performed based on 999 replications at the 5

t1 <- nptestind ( y1 + y2 + y3 ~ x1 + x2 + x3 + x4 + x5, 
	data = ccr81, base = "o", rts = "n", 
	reps = 999, dots = TRUE)


# Really large data-set

data(usmanuf)
head(usmanuf)

nrow(usmanuf)
table(usmanuf$year)

# This will take some time depending on computer power

data(usmanuf)
head(usmanuf)

t2 <- nptestind ( Y ~ K + L + M, data = usmanuf, 
	subset = year >= 1999 & year <= 2000, 
	reps = 999, dots = TRUE, base = "i", rts = "v")


## End(Not run)