The Severity of Depression

In a perceptive report, "Measuring the severity of depression through a self-report inventory : A comparison of logistic, factorial and implicit models" (M. de Bonis, M. O. Lebeaux, P. de Boeck, M. Simon, P. Pichot, Journal of Affective Disorders, 22, 55-64, 1991), the authors build on previous Rasch-based research in self-reported depression inventories. The authors remark that: "Although these applications of the Rasch model are very informative, they are also incomplete for several reasons:
(a) In most articles no information is given about the numerical values of the Rasch parameters [and] no advantage is taken of the possibility the Rasch model offers to compare persons and items on the same scale.
(b) Through the analyses, items are excluded from the initial set without specifying the exact criterion.
(c) No information is given about person fit, that is, for example whether or not lack of fit is concentrated in a few persons that might have responded at random.

An even more serious drawback, when one is interested in the Rasch model for depression in general, is that, in most studies, the initial item set is selected more for its accessibility than for empirical or theoretical reasons."

In their own study, the authors compile 151 items. From these, 52 items are retained and reworded to suit the response categories "yes" or "no". These are then self-administered by 481 subjects with varying degrees of depressive symptoms.

The initial investigation is by principal-components factor analysis. The first factor accounts for 24% of the response variance, the next factor only 5.6%, so the test is found to be largely unidimensional in the factor-analytic sense. Almost all items with high loadings on the first factor have clearly depressive content.

In the first Rasch analysis of these seemingly uni-dimensional data, only 15 of the 52 items fit the model according to Molenaar's U statistic, which detects divergently discriminating items. These 15 items, "inventory R1", mainly probe psychic (subjective) symptoms. Somatic and anxiety items exhibit misfit, resulting in a "successful differentiation of anxiety from depression." Even artificial manipulation of the data cannot induce both types of items to fit simultaneously.

Person fit to R1 is investigated. 85 of the 481 subjects are flagged as problematic by the Martin Lofe chi-square and Andersen tests. "However, the item parameter values did not change by excluding these from the data." Accordingly, the entire sample is kept.

The R1 scale is then validated through the scores obtained by patients with clinically different types of depression and also with different intensities of depression. The inventory is determined to be a general depression scale without qualitative specificity.

In a sub-study, the R1 items are ranked for depressive severity by expert and naive judges. A close-to linear relationship emerges between these rankings and the Rasch item calibrations, with a .93 correlation.

Several of the original 52 items that load highly on the first factor misfit the Rasch model. This prompts a second Rasch analysis of only the 37 (= 52 - 15) omitted items. 23 items, "inventory R2", now fit the Rasch model, but their meaning seems heterogeneous. The R2 item symptomatic of the deepest depression is "I feel there is a lump in my throat." The slightest depression is flagged by "At present things worry and torment me."

The subjects' R2 scores appear to be as empirically valid as those on R1. R2 items also loaded on the first factor, though not as highly as R1. The fact that a heterogeneous set of items fit the Rasch model is in line with previous studies of depression inventories, but the item homogeneity of R1 has the virtue of making "the scores on the R1 inventory easy to interpret."

The authors conclude: "It makes sense for two reasons to find more than one Rasch scale from a single factor-analytic dimension. First the different Rasch scales can contain items with a secondary loading on different factors. This is clearly not the case for the R1 and R2 scale; there are not one or more other factors than the first that differentiate between the two scales. Second, the different Rasch dimensions can have different degrees of discrimination. Unidimensionality in the Rasch sense includes an equal degree of discrimination. Since factor loadings are an indication of the degree of discrimination along the underlying dimension, one may find different Rasch scales in a single factor if the loadings differ from scale to scale. This is what was found in the present study. The loadings of the R2 items are clearly lower than those of the R1 items. The fact that both scales refer to the same factor-analytic dimension explains why they differentiate similarly between groups of patients."

Calibration     Inventory R1: 15 Items
Most Depressed
1.77            I wish life were ended
1.62            better if I were dead

0.69            no hope for future
0.65            disgusted with myself
0.40            I feel useless

-0.12           life seems empty
-0.13           I feel blocked
-0.25           unable to decide
-0.26           no energy
-0.52           I feel blue
-0.62           I must force myself
-0.67           I feel sad
-0.67           I have difficulty doing
-0.69           less happy than most

-1.18           I work less easily
Least Depressed

The Severity of Depression, M. de Bonis et al. … Rasch Measurement Transactions, 1992, 6:3 p. 242-3

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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