Test the three core hypotheses of a hierarchical SDT model
Source:R/hypotheses.R
usdt_hypotheses.RdEvaluates the difference between average task sensitivities (H1), their
correlation across subjects (H2), and the regression of indirect sensitivity
on direct sensitivity (H3). usdt_tests() computes all three together,
while individual functions compute them separately.
Usage
usdt_tests(fit, direct = "d_D", indirect = "d_I", level = 0.95)
sensitivity_diff(fit, direct = "d_D", indirect = "d_I", level = 0.95)
latent_cor(fit, direct = "d_D", indirect = "d_I", level = 0.95)
latent_regression(fit, direct = "d_D", indirect = "d_I", level = 0.95)Arguments
- fit
A fitted model: an
hsdtobject or aglmerModfromlme4::glmer().- direct, indirect
Character strings naming the sensitivity terms in the model. Defaults match the internal naming of
hsdt(). For custom models, both terms must be fixed effects and share a common random-effects grouping by subject.- level
Confidence level for intervals (default is 0.95).
Value
A data frame with columns term, estimate, se, statistic,
p.value, conf.low, conf.high, and ci_method. Columns status and
reason flag unsupported estimates (e.g., singular fits). usdt_tests()
includes an extra hypothesis column (H1, H2, H3).
Details
These tests run automatically inside hsdt() and appear in its summary.
Calling them directly is especially useful when fitting custom models with
lme4::glmer(), allowing you to test these hypotheses while controlling for
additional covariates (e.g., set size, experimental groups).
The three hypotheses
H1 (Mean difference): Tests whether average sensitivity differs between the direct and indirect tasks.
H2 (Correlation): Tests the correlation between task sensitivities across participants using a Fisher-\(z\) transformed interval.
H3 (Latent regression): Regresses indirect sensitivity onto direct sensitivity. The intercept represents expected indirect performance when direct sensitivity is zero (\(d'_{\mathrm{Direct}} = 0\)), testing for unconscious processing.
Because both the correlation (H2) and regression slope (H3) are zero if and only if the covariance between sensitivities is zero, they evaluate the same association and share identical test statistics.
Custom models with covariates
To adjust tests for additional factors, specify the model directly using
lme4::glmer(). As long as the two sensitivity terms are included as fixed
effects and correlated across subjects via random slopes, usdt_tests() will
compute the latent tests conditional on those covariates.
Examples
# 1. Standard model via hsdt()
d <- usdt_data_tasks(
direct = vadillo_awareness,
indirect = vadillo_cuing,
subject_col = "subj",
condition_col = "condition",
condition_levels = c(signal = "old", noise = "new"),
response_col = list(direct = "judged.old", indirect = "rt"),
response_levels = list(direct = c(signal = 1, noise = 0),
indirect = c(signal = "faster", noise = "slower")),
dichotomize = list(direct = FALSE, indirect = TRUE)
)
m <- hsdt(d)
# All three tests at once
usdt_tests(m)
#> hypothesis term estimate se statistic
#> 1 H1 d'(indirect) - d'(direct) -0.10712457 0.03537881 -3.0279299
#> 2 H2 correlation 0.49116444 0.51904281 1.0090130
#> 3 H3 intercept 0.04446212 0.11597753 0.3833684
#> 4 H3 slope 0.35605319 0.48703535 1.0090130
#> p.value conf.low conf.high ci_method status reason
#> 1 0.002462352 -0.1764658 -0.03778337 Wald ok <NA>
#> 2 0.312968398 -0.6657983 0.95434470 Fisher-z ok <NA>
#> 3 0.701446664 -0.1828497 0.27177390 delta ok <NA>
#> 4 0.312968398 -0.5985186 1.31062494 Wald ok <NA>
# Or one test at a time
sensitivity_diff(m) # H1
#> term estimate se statistic p.value
#> 1 d'(indirect) - d'(direct) -0.1071246 0.03537881 -3.02793 0.002462352
#> conf.low conf.high ci_method status reason
#> 1 -0.1764658 -0.03778337 Wald ok <NA>
latent_cor(m) # H2
#> term estimate se statistic p.value conf.low conf.high
#> 1 correlation 0.4911644 0.5190428 1.009013 0.3129684 -0.6657983 0.9543447
#> ci_method status reason
#> 1 Fisher-z ok <NA>
latent_regression(m) # H3
#> term estimate se statistic p.value conf.low conf.high
#> 1 intercept 0.04446212 0.1159775 0.3833684 0.7014467 -0.1828497 0.2717739
#> 2 slope 0.35605319 0.4870354 1.0090130 0.3129684 -0.5985186 1.3106249
#> ci_method status reason
#> 1 delta ok <NA>
#> 2 Wald ok <NA>
# \donttest{
# 2. Custom model with covariates via glmer()
# Controlling for display set size across both tasks
trials <- rbind(
data.frame(vadillo_awareness[c("subj", "condition", "set.size")],
task = "D", resp = vadillo_awareness$judged.old),
data.frame(vadillo_cuing[c("subj", "condition", "set.size")],
task = "I", resp = meyen_split(vadillo_cuing$rt,
by = vadillo_cuing$subj))
)
# Deviation contrasts (-0.5 vs 0.5); `direct` flags the direct task
trials <- within(trials, {
cond <- ifelse(condition == "old", 0.5, -0.5)
size <- ifelse(set.size == "set size 16", 0.5, -0.5)
direct <- as.integer(task == "D")
})
# Standard glmer formula: indirect criterion is omitted (fixed at 0
# by the median split). Random effects estimate the direct criterion
# and correlated task sensitivities across subjects.
fit <- lme4::glmer(
resp ~ 0 + direct + task:size + task:cond +
(0 + direct | subj) + (0 + task:cond | subj),
data = trials, family = binomial("probit"),
control = lme4::glmerControl(optimizer = "bobyqa")
)
# Check the names lme4 assigned to the sensitivity terms
names(lme4::fixef(fit))
#> [1] "direct" "taskD:size" "taskI:size" "taskD:cond" "taskI:cond"
# Evaluate hypotheses conditional on set size
usdt_tests(fit, direct = "taskD:cond", indirect = "taskI:cond")
#> hypothesis term estimate se statistic
#> 1 H1 d'(indirect) - d'(direct) -0.11543872 0.03708874 -3.1125005
#> 2 H2 correlation 0.38197036 0.39480466 0.9806745
#> 3 H3 intercept 0.07360717 0.07328775 1.0043583
#> 4 H3 slope 0.24018109 0.28657808 0.9806745
#> p.value conf.low conf.high ci_method status reason
#> 1 0.001855097 -0.18813131 -0.04274613 Wald ok <NA>
#> 2 0.326753304 -0.46496183 0.86385791 Fisher-z ok <NA>
#> 3 0.315205936 -0.07003419 0.21724852 delta ok <NA>
#> 4 0.326753304 -0.32150163 0.80186381 Wald ok <NA>
# }