R — R2noharm" />
R2noharm.Rd
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).
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, ...)
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 |
model.type | Can be |
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 |
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 ( |
display | Display output? |
object | Object of class |
logfile | File name if the summary should be sunk into a file |
... | Further arguments to be passed |
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/
A list with following entries
Tanaka index
RMSR statistic
Sample sizes of pairwise item observations
Product moment matrix
Used student weights
Fixed guessing parameters
Residual covariance matrix
Vector of final constants
Threshold parameters
Item uniquenesses
Matrix of loadings in theta parametrization (common factor parametrization)
Covariance matrix of factors
Item difficulties (for unidimensional models)
Item discriminations (for unidimensional models)
Loading matrix (latent trait parametrization)
Used model type
Number of observations
Number of items
Model type according to the NOHARM specification (see NOHARM manual)
Initial loading matrix for \(F\)
Pattern loading matrix for \(F\)
Initial covariance matrix for \(P\)
Pattern covariance matrix for \(P\)
Original data frame
System time
Used NOHARM directory
Number of digits in product moment matrix
Used decimal symbol
Number of digits for fit display
Number of dimensions
Statistic \(\chi^2\)
Number of estimated parameters
Degrees of freedom
Ratio \(\chi^2 / df\)
RMSEA statistic
Significance for \(\chi^2\) statistic
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
Possible errors often occur due to wrong dec
specification.
For estimating standard errors see R2noharm.jackknife
.
For EAP person parameter estimates see R2noharm.EAP
.
For an R implementation of the NOHARM model see noharm.sirt
.