polychoric

From poly- +‎ choric.

polychoric (not comparable)

1. (music) Of or pertaining to the use of more than one chorus; that uses or is intended to use more than one chorus.
   • 1962, Brass Quarterly, volumes 5-6, page 116:

     The polychoric motets of the Venetian school (Willaert, the Gabrielis, etc., some of whose motets are found in CW vol. 10 and IM vols. 1-2) furnish striking possibilities for multiple brass choirs.

   • 1988, Harold Gleason, Warren Becker, Catherine Gleason, Music in the Middle Ages and Renaissance, page 142:

     The brilliant polychoric canzona has contrasting sections of imitation and homophony; this evolved into the Baroque sonata.

   • 1990, Jon Michael Spencer, Protest & Praise: Sacred Music of Black Religion, page 235:

     Here, a spatial polychoric effect is attained in an acoustical polarity between the deaconesses and missionaries in the "hallelujah corner" and the deacons in the "amen corner," or in churches where the seating arrangement is segregated by gender.

2. (statistics) Of or pertaining to the relationship between two latent variables, each assumed to have a normal distribution and associated with an ordinal variable.
   • 2007, Bruno D. Zumbo, 3: Validity: Foundation Issues and Statistical Methodology, C. R. Rao, S. Sinharay (editors), Handbook of Statistics, Volume 26: Psychometrics, page 66,

     Because the CES-D items are ordinal in nature (i.e., in our case a four-point response scale, and hence not continuous), a polychoric covariance matrix was used as input for the analyses.

   • 2008, Emily Anton Bobrow, Factors that influence disclosure and program participation among pregnant HIV-positive women, page 57:

     Socioeconomic status (SES) was represented by a factor score derived using the polychoric method, which is a variation on the principle component analysis procedure designed for use with dichotomous and categorical variables (Kolenikov S, 2004).

   • 2010, William H. Greene, David A. Hensher, Modeling Ordered Choices: A Primer, page 294:

     The polychoric correlation coefficient is an estimator of the correlation coefficient in the underlying bivariate normal distribution.

   • 2010, Adriana Rocío Cardozo Silva, Economic Growth and Poverty Reduction in Colombia, page 49:

     The authors propose using polychoric correlations in order to estimate the correlation matrix before using PCA.^{[Principal Component Analysis]} Polychoric PCA assumes that the observed ordinal variable has an underlying continuous variable and uses maximum likelihood to calculate how that continuous value would have to be split up in order to produce the observed data.

The statistics term occurs chiefly in the collocation polychoric correlation.

• polychoric correlation

• polychoron
• tetrachoric (statistics, a special case)

polychoric (plural polychorics)

1. A polychoric correlation

• polyserial

• polychroic