This function provides assesses the homogeneity of the diagnosticity ratio of k lineup pairs.
Arguments
- lineup_pres_list
A list containing k vectors of lineup choices for k lineups, in which the target was present
- lineup_abs_list
A list containing k vectors of lineup choices for k lineups, in which the target was absent
- pos_list
Suspect positions for each lineup pair. See
diag_param().- k
A vector indexing number of members in each lineup pair (nominal size). Must be specified by user (scalar).
- conf.level
Confidence level for the per-pair intervals, and the complement of the level at which heterogeneity is declared. Defaults to 0.95.
Value
Invisibly, a list with the pooled (precision-weighted) diagnosticity
ratio, the chi-square statistic and its degrees of freedom and p-value,
a heterogeneous flag, and a parameters data frame giving
the cell counts plus \(d\), \(\ln d\), its variance, its weight and
a confidence interval for each lineup pair. The same information is
printed.
Details
Master function for assessing homogeneity of diagnosticity ratio for k independent lineups.
The chi-square is Cochran's Q, \(\sum w_i (\ln d_i - \ln \bar{d})^2\),
so it measures the spread of the k ratios around their pooled
value. It answers a different question from a confidence interval on
the pooled ratio, which asks whether the average ratio differs from 1.
The two can disagree: ratios that differ in direction (say 6, 1 and
0.44) give a very large Q while averaging to roughly 1. When Q is
significant the ratios do not share a common value, the pooled
estimate should not be reported as a single summary, and the pairs
should be interpreted separately. This function prints a note to that
effect and records it in the heterogeneous element.
References
Malpass, R. S. (1981). Effective size and defendant bias in eyewitness identification lineups. Law and Human Behavior, 5(4), 299-309.
Malpass, R. S., Tredoux, C., & McQuiston-Surrett, D. (2007). Lineup construction and lineup fairness. In R. Lindsay, D. F. Ross, J. D. Read, & M. P. Toglia (Eds.), Handbook of Eyewitness Psychology, Vol. 2: Memory for people (pp. 155-178). Mahwah, NJ: Lawrence Erlbaum Associates.
Tredoux, C. G. (1998). Statistical inference on measures of lineup fairness. Law and Human Behavior, 22(2), 217-237.
Tredoux, C. (1999). Statistical considerations when determining measures of lineup size and lineup bias. Applied Cognitive Psychology, 13, S9-S26.
Wells, G. L.,Leippe, M. R., & Ostrom, T. M. (1979). Guidelines for empirically assessing the fairness of a lineup. Law and Human Behavior, 3(4), 285-293.
Examples
#Target present data:
A <- rep(1:6, length.out = 100)
B <- rep(1:5, length.out = 70)
C <- rep(1:4, length.out = 20)
lineup_pres_list <- list(A, B, C)
rm(A, B, C)
#Target absent data:
A <- rep(6:1, length.out = 100)
B <- rep(5:1, length.out = 70)
C <- rep(4:1, length.out = 20)
lineup_abs_list <- list(A, B, C)
rm(A, B, C)
# Suspect position for each TP/TA pair
pos_list <- c(3, 2, 1)
#Nominal size:
k <- c(6, 5, 4)
#Call:
homog_diag(lineup_pres_list, lineup_abs_list, pos_list, k)
#> Diagnosticity ratio for each lineup pair:
#> pair d 95% CI
#> 1 1.000 [0.54, 1.84]
#> 2 1.000 [0.52, 1.94]
#> 3 1.000 [0.34, 2.93]
#>
#> Mean diagnosticity ratio: 1
#> Chi-square estimate (q): 0
#> Sig: 1
#>
#> Note: no evidence of heterogeneity (p >= 0.05), so the ratios are
#> consistent with a common value and the pooled mean is a reasonable summary.