Confidence intervals for HiTOP-BR scale scores — interval

Converts scored HiTOP-BR columns into a regression-based true-score estimate and a confidence interval around it, using the development-sample mean, standard deviation and reliability shipped as hitopbr_devstats. This function converts already-scored columns and never rescores: the 8 scale columns score_hitopbr() produces are the ones it is built for, and hitopbr_devstats carries a row for each of them.

Usage

interval_hitopbr(
  data,
  scores,
  srange = c(1, 4),
  prefix = "hbr_",
  level = 0.95,
  append = TRUE
)

Arguments

data: A data frame containing scored HiTOP-BR columns.
scores: The score columns to convert, as column names or column positions (mirroring the items argument of score_hitopbr()). Each column must be numeric (or logical) and each may be named only once.
srange: The response range the items were scored on, as c(low, high). The reference statistics are printed on the official four-option c(1, 4) coding; any other coding is a different metric. See Details.
prefix: The prefix score_hitopbr() applied to its output columns, used to match a score column back to its scale. Matched literally, not as a regular expression: a column name that does not begin with exactly this string keeps its whole name and is reported as uncovered. Pass "" when the columns are named for the scales themselves, with no prefix to strip.
level: The confidence level, as a proportion between 0 and 1. Defaults to 0.95.
append: Whether to return the input data with the interval columns appended (TRUE, the default) or the interval columns alone.

Value

A tibble with an _est, _lo and _hi column for every requested score column, alongside all original data columns if requested. An NA score returns NA in all three.

Details

What is computed. For a score $x$ on a scale whose reference group has mean $M$, standard deviation $SD$ and reliability $r$, the estimate and bounds are Schmukle's (2026) Equations (10) to (12), p. 821:

$$est = M + \sqrt{r}\,(x - M)$$ $$SEM = SD \sqrt{1 - r}$$ $$lo,\ hi = est \pm z\,SEM$$

where $z$ is the two-sided standard normal quantile for level (1.959964 at the default 0.95). The estimate is the observed score pulled toward the reference mean, because with imperfect measurement a true score tends to lie nearer the mean than the observed score does; the $\sqrt{r}$ factor is Schmukle's scale correction, which returns the estimate to the metric the observed score is on so the two can be read against each other.

The reference group is a development sample. hitopbr_devstats carries the statistics printed for the HiTOP-SR introduction paper's Development Sample 2: N = 780 Prolific Academic participants stratified by sex and age to approximate a community-representative United States population. That is a development sample and not a community norm – no census weighting was applied and no raw-score to T-score table is published – so an interval from this function says where a score sits relative to the sample the instrument was developed on, and not what percentile it occupies in any population.

Two limitations worth stating. Equation (12)'s interval is symmetric about the estimate and the same width for every respondent on a given scale, which is what classical test theory implies and what the source computes. On a floor-heavy scale that width can put a bound outside the response range, and the bounds are not clamped, because clamping would report something other than the equation this function cites. Every HiTOP-BR scale is floor-heavy enough for this to bite: on all eight, a score of 1 – the response floor – returns a lower bound below 1. And the coverage Schmukle demonstrates is marginal: over a population of respondents drawn from the reference distribution, about level of the intervals contain the true score. It is established under a linear measurement model with approximately normal item responses, so it is not a guarantee for any one respondent, nor a demonstration on scales as skewed as these.

The scales overlap. Externalizing and p-Factor are drawn from the same items as the six spectrum scales rather than added to them, so a respondent contributes the same answers to several of these intervals. Read them as eight views of one response set, not as eight independent measurements.

Reporting and silence. Both things this function reports are warning conditions, so a single suppressWarnings() call silences it and either report can still be caught and tested for on its own.

A score column with no hitopbr_devstats row returns NA in all three columns, with a warning of class hitop_interval_uncovered naming the columns. A column is matched by stripping prefix and looking the rest up in hitopbr_devstats$camelCase, so this fires for a mistyped prefix as well as for a column that is not a HiTOP-BR scale score.
A call whose srange is not the c(1, 4) coding the reference mean and standard deviation are printed on returns NA in every interval column, with a warning of class hitop_interval_coding. Nothing is reconciled: a shift or a stretch of the response range moves a scale score, and no mapping from another coding onto these statistics is published.

Partly scored scales are not detected. A score computed from fewer than a scale's full items – from data with items missing under missing = "available" – is not on the same footing as the reference statistics, which come from complete scales. This function receives scores and not items, so it cannot tell such a column from a fully scored one and does not try: it converts what it is given. Treat an interval on a partly scored scale as not comparable to the reference group.

Errors. scores is checked before anything is converted. Naming the same score column twice is an error rather than a duplicated set of output columns, and a factor or character score column is an error rather than a silent coercion – a factor's integer codes are not its scores, and a character column would coerce to NA. Logical columns are accepted.

A scores argument that names no columns is an error, reported ahead of the other selection arguments, so the cause named is the empty selection and not a consequence of it. The condition is classed hitop_empty_selection, so a caller can catch this refusal by name.

With append = TRUE, a column of data whose name this call would also produce is an error rather than an overwrite or a duplicated column: the message names every colliding column. Re-run with append = FALSE to return only the new columns, or drop the colliding columns from data first. The condition is classed hitop_append_collision, so a caller can catch this refusal by name.

References

Schmukle, S. C. (2026). Unbiased confidence intervals for psychological testing: The regression-based true score approach with scale correction. Assessment, 33(5), 817-825. Equations (10) to (12), p. 821, are what this function computes; Box 1, p. 823, works two examples.

Examples

# Score the HiTOP-BR, then put an interval around two scales
scored <- score_hitopbr(sim_hitopbr, items = 1:45)
interval_hitopbr(
  scored,
  scores = c("hbr_detachment", "hbr_pFactor"),
  append = FALSE
)
#> # A tibble: 100 × 6
#>    hbr_detachment_est hbr_detachment_lo hbr_detachment_hi hbr_pFactor_est
#>                 <dbl>             <dbl>             <dbl>           <dbl>
#>  1               2.75             2.11               3.40            2.36
#>  2               1.64             0.993              2.28            1.98
#>  3               2.75             2.11               3.40            2.29
#>  4               2.57             1.92               3.21            1.90
#>  5               2.19             1.55               2.84            2.52
#>  6               2.38             1.74               3.03            2.59
#>  7               2.38             1.74               3.03            2.44
#>  8               2.38             1.74               3.03            2.67
#>  9               2.57             1.92               3.21            2.21
#> 10               2.19             1.55               2.84            2.67
#> # ℹ 90 more rows
#> # ℹ 2 more variables: hbr_pFactor_lo <dbl>, hbr_pFactor_hi <dbl>

# A 90% interval is narrower
interval_hitopbr(
  scored,
  scores = "hbr_detachment",
  level = 0.90,
  append = FALSE
)
#> # A tibble: 100 × 3
#>    hbr_detachment_est hbr_detachment_lo hbr_detachment_hi
#>                 <dbl>             <dbl>             <dbl>
#>  1               2.75              2.21              3.29
#>  2               1.64              1.10              2.18
#>  3               2.75              2.21              3.29
#>  4               2.57              2.02              3.11
#>  5               2.19              1.65              2.74
#>  6               2.38              1.84              2.92
#>  7               2.38              1.84              2.92
#>  8               2.38              1.84              2.92
#>  9               2.57              2.02              3.11
#> 10               2.19              1.65              2.74
#> # ℹ 90 more rows