Estimation of a NOHARM Analysis from within R

This function enables the estimation of a NOHARM analysis (Fraser & McDonald, 1988; McDonald, 1982a, 1982b, 1997) from within R. NOHARM estimates a compensatory multidimensional factor analysis for dichotomous response data. Arguments of this function strictly follow the rules of the NOHARM manual (see Fraser & McDonald, 2012; Lee & Lee, 2016).

Usage

R2noharm(dat=NULL,pm=NULL, n=NULL, model.type, weights=NULL, dimensions=NULL,
      guesses=NULL, noharm.path, F.pattern=NULL, F.init=NULL,
      P.pattern=NULL, P.init=NULL, digits.pm=4, writename=NULL,
      display.fit=5,  dec=".", display=TRUE)

# S3 method for R2noharm
summary(object, logfile=NULL, ...)

Arguments

dat: An $N \times I$ data frame of item responses for $N$ subjects and $I$ items
pm: A matrix or a vector containing product-moment correlations
n: Sample size. This value must only be included if pm is provided.
model.type: Can be "EFA" (exploratory factor analysis) or "CFA" (confirmatory factor analysis).
weights: Optional vector of student weights
dimensions: Number of dimensions in exploratory factor analysis
guesses: An optional vector of fixed guessing parameters of length $I$. In case of the default NULL, all guessing parameters are set to zero.
noharm.path: Local path where the NOHARM 4 command line 64-bit version is located.
F.pattern: Pattern matrix for $F$ ($I \times D$)
F.init: Initial matrix for $F$ ($I \times D$)
P.pattern: Pattern matrix for $P$ ($D \times D$)
P.init: Initial matrix for $P$ ($D \times D$)
digits.pm: Number of digits after decimal separator which are used for estimation
writename: Name for NOHARM input and output files
display.fit: How many digits (after decimal separator) should be used for printing results on the R console?
dec: Decimal separator ("." or ",")
display: Display output?
object: Object of class R2noharm
logfile: File name if the summary should be sunk into a file
...: Further arguments to be passed

Details

NOHARM estimates a multidimensional compensatory item response model with the probit link function $\Phi$. For item responses $X_{pi}$ of person $p$ on item $i$ the model equation is defined as $$P( X_{pi}=1 | \bold{\theta}_p )=c_i + ( 1 - c_i ) \Phi( f_{i0} + f_{i1} \theta_{p1} + ... + f_{iD} \theta_{pD} ) $$ where $F=(f_{id})$ is a loading matrix and $P$ the covariance matrix of $\bold{\theta}_p$. The guessing parameters $c_i$ must be provided as fixed values.

For the definition of $F$ and $P$ matrices, please consult the NOHARM manual.

This function needs the 64-bit command line version which can be downloaded from (some links may be broken in the meantime)

http://noharm.niagararesearch.ca/nh4cldl.html
https://noharm.software.informer.com/4.0/
https://cehs.unl.edu/edpsych/software-urls-and-other-interesting-sites/

Value

A list with following entries

tanaka: Tanaka index
rmsr: RMSR statistic
N.itempair: Sample sizes of pairwise item observations
pm: Product moment matrix
weights: Used student weights
guesses: Fixed guessing parameters
residuals: Residual covariance matrix
final.constants: Vector of final constants
thresholds: Threshold parameters
uniquenesses: Item uniquenesses
loadings.theta: Matrix of loadings in theta parametrization (common factor parametrization)
factor.cor: Covariance matrix of factors
difficulties: Item difficulties (for unidimensional models)
discriminations: Item discriminations (for unidimensional models)
loadings: Loading matrix (latent trait parametrization)
model.type: Used model type
Nobs: Number of observations
Nitems: Number of items
modtype: Model type according to the NOHARM specification (see NOHARM manual)
F.init: Initial loading matrix for $F$
F.pattern: Pattern loading matrix for $F$
P.init: Initial covariance matrix for $P$
P.pattern: Pattern covariance matrix for $P$
dat: Original data frame
systime: System time
noharm.path: Used NOHARM directory
digits.pm: Number of digits in product moment matrix
dec: Used decimal symbol
display.fit: Number of digits for fit display
dimensions: Number of dimensions
chisquare: Statistic $\chi^2$
Nestpars: Number of estimated parameters
df: Degrees of freedom
chisquare_df: Ratio $\chi^2 / df$
rmsea: RMSEA statistic
p.chisquare: Significance for $\chi^2$ statistic

References

Fraser, C., & McDonald, R. P. (1988). NOHARM: Least squares item factor analysis. Multivariate Behavioral Research, 23, 267-269. https://doi.org/10.1207/s15327906mbr2302_9

Fraser, C., & McDonald, R. P. (2012). NOHARM 4 Manual.
http://noharm.niagararesearch.ca/nh4man/nhman.html.

Lee, J. J., & Lee, M. K. (2016). An overview of the normal ogive harmonic analysis robust method (NOHARM) approach to item response theory. Tutorials in Quantitative Methods for Psychology, 12(1), 1-8. https://doi.org/10.20982/tqmp.12.1.p001

McDonald, R. P. (1982a). Linear versus nonlinear models in item response theory. Applied Psychological Measurement, 6(4), 379-396. doi:10.1177/014662168200600402

McDonald, R. P. (1982b). Unidimensional and multidimensional models for item response theory. I.R.T., C.A.T. conference, Minneapolis, 1982, Proceedings.

McDonald, R. P. (1997). Normal-ogive multidimensional model. In W. van der Linden & R. K. Hambleton (1997): Handbook of modern item response theory (pp. 257-269). New York: Springer. http://dx.doi.org/10.1007/978-1-4757-2691-6

Note

Possible errors often occur due to wrong dec specification.