Computing elementary symmetric functions and their derivatives: A didactic
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Computing elementary symmetric functions and their derivatives: A didactic
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1996
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Abstract
The computation of elementary symmetric functions
and their derivatives is an integral part of conditional
maximum likelihood estimation of item parameters under
the Rasch model. The conditional approach has the
advantages of parameter estimates that are consistent
(assuming the model is correct) and statistically rigorous
goodness-of-fit tests. Despite these characteristics, the
conditional approach has been limited by problems in
computing the elementary symmetric functions. The introduction
of recursive formulas for computing these
functions and the availability of modem computers has
largely mediated these problems; however, detailed
documentation of how these formulas work is lacking.
This paper describes how various recursion formulas
work and how they are used to compute elementary
symmetric functions and their derivatives. The availability
of this information should promote a more thorough
understanding of item parameter estimation in the Rasch
model among both measurement specialists and
practitioners. Index terms: algorithms, computational
techniques, conditional maximum likelihood, elementary
symmetric functions, Rasch model.
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Previously Published Citation
Baker, Frank B & Harwell, Michael R. (1996). Computing elementary symmetric functions and their derivatives: A didactic. Applied Psychological Measurement, 20, 169-192. doi:10.1177/014662169602000206
Suggested citation
Baker, Frank B.; Harwell, Michael R.. (1996). Computing elementary symmetric functions and their derivatives: A didactic. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/119090.
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