2.2. Analysis
Contrast sensitivity data were submitted to a Type III sums-of-squares 2
(spatial frequency) x 2 (subject group) mixed-model analysis of variance
(ANOVA); this was done once with the raw contrast sensitivity data and
once again with the log-transformed data. In each case, a
Greenhouse-Geisser correction was applied to account for violation of
the sphericity assumption (Mauchly’s test). In all cases, follow-up
t-tests assumed equal variances unless a significant Levene’s test
required otherwise. Note that we simplified the analyses by examining
only the two most extreme spatial frequency conditions–0.5 and 21
cycles per degree–since the former has been claimed to most clearly
bias processing toward the magnocellular stream and the latter toward
the parvocellular stream and since group interaction effects should be
clearly observed at these endpoints (Butler et al., 2005). Note also
that we confined our results only to the shortest stimulus duration (33
ms) since these stimulus types have been used in previous schizophrenia
studies that sought to bias processing toward the magnocellular channel
(Butler et al., 2005; Martinez et al., 2012; Revheim et al., 2014).
Nevertheless, we also (and separately) analyzed the 500 ms stimulus
duration data for completeness.
To corroborate the log-transformed results, we performed generalized
estimating equations (GEE) analysis using the raw (non-transformed)
contrast sensitivity data. The analysis incorporated a gamma
distribution function with a log link (to reflect the relationship of
mean and variance in contrast sensitivity data), robust estimators of
the standard errors, a maximum likelihood estimation of the parameters,
and an exchangeable correlation structure (since conditions were
counterbalanced). GEE’s advantage over generalized linear mixed models
(GLMMs) is that it can handle heteroscedasticity, does not require
correct specification of the covariance structure, makes fewer
assumptions, and is more robust when only population-level (marginal)
effects are desired (Pekár & Brabec, 2018).
To consider the role of visual acuity, we also conducted analyses that
matched groups on acuity (Elliot, 2016) and included this variable as a
covariate. We opted to remove high-acuity controls rather than
lower-acuity patients since i) poor acuity may characterize the illness
(Hayes et al., 2018; Shoham et al., 2021), ii) most healthy people with
poor acuity never develop psychosis; and iii) it is inappropriate to add
an illness-related covariate when the groups are not matched on the
covariate (Miller & Chapman, 2001). Potential issues with
interpretability of visual acuity confounds are further considered in
the Discussion.