Item response theory applied to the Beck Depression Inventory

Abstracts

O Inventário de Depressão Beck (BDI), uma escala que mede o traço latente de intensidade de sintomas depressivos, pode ser avaliado através da Teoria da Resposta ao Item (TRI). Este estudo utilizou o modelo TRI de Resposta Gradual na avaliação da intensidade de sintomas depressivos de 4.025 indivíduos que responderam ao BDI, de modo a explorar eficientemente a informação disponível nos diferentes aspectos possibilitados pelo uso desta metodologia. O ajuste foi efetuado no software PARSCALE. Foram identificados 13 itens do BDI nos quais pelo menos uma categoria de resposta não tinha chance maior que as demais de ser escolhida, de modo que estes itens tiveram de ser recategorizados. Os itens com maior capacidade de discriminação são relativos à tristeza, pessimismo, sentimento de fracasso, insatisfação, auto-aversão, indecisão e dificuldade para trabalhar. Os itens mais graves são aqueles relacionados com perda de peso, retraimento social e idéias suicidas. O grupo dos 202 indivíduos com as maiores intensidades de sintomas depressivos foi composto por 74% de mulheres, e praticamente 84% possuíam diagnóstico de algum transtorno psiquiátrico. Os resultados evidenciam alguns dos inúmeros ganhos advindos da utilização da TRI na análise de traços latentes.

Teoria da Resposta ao Item; Traço latente; Intensidade de sintomas depressivos; Inventário de Depressão Beck

SPECIAL ARTICLE

Universidade Federal do Rio Grande do Sul

Correspondência

ABSTRACT

The Beck Depression Inventory (BDI), a scale that measures the latent trait intensity of depression symptoms, can be assessed by the Item Response Theory (IRT). This study used the Graded-Response model (GRM) to assess the intensity of depressive symptoms in 4,025 individuals who responded to the BDI, in order to efficiently use the information available on different aspects enabled by the use of this methodology. The fit of this model was done in PARSCALE software. We identified 13 items of the BDI in which at least one response category was not more likely than others to be chosen, so that these items had to be categorized again. The items with greater power of discrimination were sadness, pessimism, feeling of failure, dissatisfaction, self-hatred, indecision, and difficulty of work. The most serious items were weight loss, suicidal ideas, and social withdrawal. The group of 202 individuals with the highest levels of depressive symptoms was comprised by 74% of women and almost 84% had a diagnosis of a psychiatric disorder. The results show gains resulting from use of IRT in the analysis of latent traits.

Keywords: Item Response Theory. Latent trait. Intensity of depressive symptoms. Beck Depression Inventory.

Introduction

Latent variables, also termed latent traits, are non-observable quantities which must be inferred by observation of secondary variables associated with them. For this purpose, measurement procedures (scales) are generally used. They consist of a set of items, the responses to which are categories (ordered or otherwise) that are used to estimate the secondary variables, which in turn give estimates of a subject's latent traits.

The Beck Depression Inventory (BDI) is one example of such a measurement procedure. It consists of a group of items intended to assess the latent trait intensity of depressive symptoms; this is extremely important for establishing level of depression, and for predicting its likely outcome. Depression is a very common psychological, social and biological condition; epidemiological studies show that it affects between 3 and 11% of the general population^2,3 and that it is a lifetime condition for 16.2%³. In Brazil, studies show that depression occurs throughout the lives of between 2.8 and 19.2% of people.

Until recently, the most commonly used statistical model for latent trait prediction was the Classical Test Theory (CTT)⁶, which uses a subject's total score as the estimate of a particular latent trait. This methodology has been reviewed by DeVellis⁷. Despite its great importance and the convenience of CTT use, a number of authors have drawn attention to its limitations, all of which are avoided by using the alternative measurement procedure known as Item Response Theory⁹.

Largely used in psychiatry, the Item Response Theory (IRT) comprises a group of generalized linear models and associated statistical procedures which describe the association between item responses (such as an individual's behavior) and a latent trait. The aim of an IRT model is to link one individual to one item. The individual's pattern of response to a particular group of items provides the basis for estimating the latent trait. In IRT models, item parameters and the subject's latent trait levels are independent of each other; these parameters are expressed by the level of response observed for the item; the contribution of each item to the final scale is determined by the IRT information; there are powerful methods available for detecting differential item functioning (DIF) or item biases between populations or subgroups; and scores given by different subjects can be compared even when they have answered to different items¹³.

IRT is particularly significant for the analysis of latent traits since it allows more efficient use of information, not only because the method groups individuals according to their latent traits, but also because it provides information about the measuring procedures themselves and, in particular, about each item used. IRT is therefore a more sophisticated method making more thorough use of the information available in each item and so giving improved measures of latent trait, since different items can be given specific degrees of importance according to their relevance to the trait being studied.

IRT models can be further categorized as cumulative or unfolding. Cumulative IRT models can be classified according to their dimensionality (unidimensional or multidimensional). Unidimensional IRT models describe the connection between observed item responses and a single underlying latent trait, usually represented by θ. They are suitable for data in which a single common factor is assessed by the items. Unidimensional models include models for dichotomous data (such as where symptoms of depression are either present or absent; or success or failure) and models for polytomous data (items with more than two response categories for each BDI item). Such models can also be distinguished according to the number of parameters used. They may have one, two or three parameters: one related to item complexity (gravity of depressive symptoms in the case of BDI), another related to item discrimination, and a third representing the probability that subjects exhibit the depressive symptom described by the item, even when the level of the latent trait is low.

All BDI items have four response categories, so that a unidimensional model for polytomous responses is appropriate. It is also unlikely that each of the 21 BDI items will discriminate equally well, for the latent trait, in every individual of a population; a model allowing each item to have a different discriminatory value, having a discrimination parameter for each item, is therefore an advantage. With this in mind, the objective of the present study is to explore the IRT Graded Response Model of Samejima¹⁴ by using it to assess the intensity of depressive symptoms in individuals that have responded to the BDI, to make full use of the information given by this method.

Methods

Data sources

Subjects were taken from a cross-sectional study designed to adapt, normalize and validate a Portuguese version on the Beck Scale, made by Dra. Jurema Alcides Cunha and published in 2001¹⁵. The 4025 individuals taking part in the study are divided in three groups: group 1, consisting of psychiatric patients (n = 1138); group 2, patients undergoing medical treatment (n = 490); group 3, subjects not under medical treatment, drawn from the population at large (n = 2397). All of them responded to the BDI, consisting of a self-evaluated scale of 21 items, each with four assertions corresponding to increasing levels of depressive symptoms¹⁵ and with scores ranging from 0 to 3. BDI items were chosen based on the most commonly observed behavior and attitudes reported in psychiatric patients with symptoms of depression¹⁵: sadness; pessimism; feelings of failure; dissatisfaction; guilt; punishment; self-hatred; self-accusation; suicidal thoughts; weeping; irritability; social withdrawal; indecision; changes in self-awareness; work difficulties; insomnia; fatigue; weight loss; somatic worries; loss of libido. A total score varying between 0 and 63 was used in the study¹⁵ to estimate the intensity of subjects' depressive symptoms, so that the following intervals were defined to distinguish between the degree of symptom severity in different subjects: minimal (0-11), light (12-19), moderate (20-35) and heavy (36-63). As the IRT scores (estimating the intensity of depressive symptoms, in the graded response model) have zero mean and unit Standard deviation (i.e., are on scale (0,1)), a linear transformation is applicable, giving a change in scale on which IRT score can be related to total score, based on which individuals have been classified according to the intensity of their depressive symptoms.

Theory of Item Response^16,17.

An IRT polytomous model suitable for BDI data is the Graded Response Model (GRM) proposed in 1969 by Samejima¹⁴, which assumes that an item's response categories can be ordered. When fitting the GRM, the items in the procedure need not have the same number of response categories.

The response categories of an item are arranged with their scores in increasing order, denoted by k=0,1,2...m_i, where (m_i+1) is the number of categories for the i-th item. Then the probability that the j-th subject chooses a given category i, or one larger than it, is given by

where i=1,2,...,I, j=1,2,...,n, k=1,2,...,m_i and b_i,1 < b_i,2 < ... < b_i,mi; θ_i is the intensity of depressive symptoms (the latent trait) of the j-th subject; a_i is common slope parameter for all categories of item i; b_i,k is the location parameter (a point on the latent trait continuum) for the k-th category of item i, i.e., each b_i,k is the point of intersection amongst the categories of ordered responses, representing the degree of intensity of depressive symptoms needed for response category greater than or equal to the k-th to be chosen with equal probability 0.5; D is a scale factor equal to 1 or 1.7, the latter value pertaining when the logistic function is required to give results similar to those of the Normal distribution.

The probability that subject j responds to category k of item i is given by the difference

where by definition and

Therefore

The curves generated by (1) are termed Response Category Curves. They show the relationship between the response probabilities for the categories of each item and the level of latent trait, and from them it is possible to determine which response category has the highest probability of being chosen for each latent trait level.

The GRM was fitted using the software PARSCALE¹⁸ version 4.1. This estimates the parameters of the GRM such that the b_i,k between categories are partitioned into two terms, one being the location parameter (b_i) for each item, and a group of parameters c_i,k for each item, so that b_i,k= b_i-c_k. In the case of the latent trait for Intensity of Depressive Symptoms, the location parameters (b_i) can be interpreted as a measure of the symptom severity measured by a given item¹⁹, and the parameters c_i,k represent the distances between the points of intersection between the response category curves for each item.

The scale on which estimates of depressive symptom intensity (termed the IRT scores) are measured is arbitrary, the important feature being the order relationship between points on the scale, and not necessarily their magnitude. They can therefore take any real value between -" and +", it being necessary to define an origin for measurement and a unit on the measurement scale. Here, the IRT scores were defined to have zero mean and unit Standard deviation ((0,1) scale). The parameter for symptom severity, b_i, is measured in the same units as the IRT scores, and so can be compared with them.

Figure 1(a) shows a graph of this model for item 1 (sadness) in the BDI, with four response categories measuring the intensity of depressive symptoms, and the following parameter estimates: â₁ = 1.478, b^_1,1 = 0.153,_1,2 = 1.280 and _1,3 = 1.897, where the response categories are:

1 I do not feel sad.

2 I feel sad.

3 I am always sad and can never shake it off.

4 I am so sad or unhappy that I cannot bear it.

It can be seen from this figure that subjects with intensity of depressive symptoms up to 0.153 are more likely to respond in category 1 (curve 1); subjects with intensity of depressive symptoms between 0.153 and 1.280 are more likely to respond in category 2 (curve 2), and subjects with intensity of depressive symptoms between 1.280 and 1.897 are more likely to choose category 3 (curve 3). Finally, subjects most likely to respond in category 4 (curve 4) are those with intensity of depressive symptoms greater than 1.897.

IRT models also yield Item Information Curves, which are widely used in conjunction with Category of Response Curves and the Test Information Curve. Using Item Information Curves, which are constructed from the information functions for each item, it is possible to analyze how much information on the measure of latent trait is contained in a given item; i.e., the curves show how much psychometric information a given depressive symptom contributes to the measure of intensity of depressive symptoms and, moreover, in which interval of this measure the symptom is most informative. It is with this characteristic that one can evaluate which depressive symptoms best discriminate within the population with regard to the intensity of depressive symptoms¹⁷. In polytomous IRT models, the quantity of information yielded by an item depends on both the magnitude of the slope parameter a_i and the distribution of points of intersection between the response categories b_i,k along the latent trait continuum. For example, the information curve for item 1 of the BDI, in Figure 1(b), shows that greatest concentration of information lies between 0.7 and 1.7 on the intensity scale of depressive symptoms. This shows that the depressive symptom 'Sadness' best discriminates between subjects whose intensity of depressive symptoms lie in this interval.

The Test Information Curve is a graphic representation of the information function. This is an additive function defined over the group of items which constitute the test (the BDI for example) which summarizes the contribution of each item to the information total. The total quantity of information yielded by a group of items at each latent trait level is inversely related to the standard error of its estimate. The test information function is a viable alternative to the concepts of confidence intervals and Standard errors in the Classical Theory of Tests, and by using the Test Information Curve one can determine in which latent trait interval the test works best.

Model assumptions.

For the GRM to be adequate, two assumptions must be satisfied: local independence (meaning that when the levels of latent trait are held constant, the response yielded by any item is unrelated to the response yielded by the preceding item) and unidimensionality (all items in the test procedure exhibit the same latent trait). The two assumptions are related, implying that when a procedure is unidimensional, it also exhibits local independence; i.e., if the assumption of unidimensionality is satisfied, only a single latent trait is influencing responses to the items, and local independence is assured^16,20. There is evidence that the assumption of unidimensionality can be relaxed, and that it need only be sufficient^21-24; i.e., it is enough for one factor to be preponderant (such that the proportion of variance explained by the first factor in a principal component analysis is not less than 20%²¹) for IRT models to be usable. In view of this, the unidimensionality of the BDI was evaluated using the procedure termed Parallel Analysis^20,25-28, available in a macro²⁹ of SAS version 9.1.3 (SAS Institute, Cary, NC, USA). This procedure involves a comparison of the eigenvalues of a principal component analysis of real data with a statistic summarizing the eigenvalues of samples of simulated data having the same number of observations and variables as the real data-set (in this case, 4 025 observations on 21 variables). The simulated samples are uncorrelated and are generated by Monte Carlo methods (5000 samples were generated and the summary statistic was the median).

Results

Demographic characteristics of the sample are shown in Table 1. Just under half the subjects are men, with slightly more women. Almost all individuals defined themselves as white, and slightly more than half are single. In terms of education, subjects are distributed almost evenly between categories up to the completion of secondary school, subjects with higher education being less frequent. The mean age of subjects is about 32 (Standard deviation 15.1 years) but the group undergoing medical treatment group is older, on average.

Results of the parallel analysis showed that the assumption of unidimensionality is adequate^19,30 because a preponderant factor was found which explained 38.7% of the total variation.

Based on curves derived from expression (1), fitting the Gradual Response model showed that for 13 of the 21 BDI items, at least one of the response categories has no probability greater than the others of being selected for any intensity of depressive symptoms, as demonstrated in Figure 2(a) for the item associated with pessimism (item 2). One possible explanation for this is that items related to pessimism, dissatisfaction, guilt, punishment, suicidal thoughts, weeping, irritability, changes in self-awareness, insomnia, appetite loss, weight loss, somatic worries and the loss of libido could be presenting problems of understanding the scale. These items were therefore re-categorized by combining together the categories adjacent to the problematic category, thus giving a scale with items having a different number of response categories. The Gradual Response model was then re-fitted, giving category of response curves which showed that all response categories have a chance of being selected for some interval in the latent trait continuum (Figure 2(b)). When the Gradual Response model was fitted with BDI items re-categorized, the estimates of model parameters were as shown in Table 2.

From the Item Information Curves, which are strongly influenced by the slope parameter (a_i in Table 2), it can be seen that when the cutoff point is defined as unity^16,19 for estimates of this parameter, so as to identify which items give good discrimination (a_i > 1), those items relating to sadness, pessimism, feelings of failure, dissatisfaction, self-hatred, indecision and work difficulties (items 1, 2, 3, 4, 7, 13 and 15 respectively) contribute most to the measure of depressive symptom intensity, and therefore give best discrimination in the population for this latent trait. It should be noted that items related to guilt (item 5) and suicidal thoughts (item 9) also have slope parameters greater than one (â₅ = 1.172 and â₉ = 1.078 in Table 2); however, the item information curves show that these items give poor discrimination. The item related to irritability (item 11) contributes least to the measure of depressive symptom intensity. Drawing a horizontal line from the point at which the item information function has value one, it can be seen that the item related to feelings of failure gives better discrimination for intensity of depressive symptoms in the population, when the IRT score is in the range [0.7;2], which corresponds approximately to the interval [21;35] on the scale for total score.

The item related to Sadness discriminates best when the IRT score lies between 0.7 and 1.7, corresponding to the total score interval 21 to 32. To convert IRT scores to the scale for total score, the former were multiplied by the Standard deviation of total score and then added to its mean value.

Estimates of the parameter for gravity of depressive symptoms (b_i in Table 2) show that items related to loss of weight, social withdrawal and suicidal thoughts are considered more severe when estimating the intensity of depressive symptoms.

Levels of intensity of depressive symptoms estimated from the Gradual Response model (IRT scores) have the same severity scale as the BDI items, so that both groups are comparable. The 95% percentile for the level of intensity of depressive symptoms is 1.6, corresponding to a total score of 31. The group with higher IRT scores is formed by 202 subjects, corresponding to 5% of the analyzed population. Table 3 illustrates this group's profile: about 84% belong to the psychiatric group; the mean age is 39 years; 74% are women; roughly half studied for less than five years, and around 40% are married.

The Test Information Curve shows that the BDI is most efficient for individuals having intensity of depressive symptoms between 0.8 and 2.4, corresponding to an interval of 22 to 40 on the scale of total score.

Discussion

The 21 items of the BDI are representive of the symptoms most frequently observed in depressed people¹⁵. Evaluation of these items in terms of the amount psychometric information that they provide, and in terms of the severity of the latent trait being measured, is a significant advantage that IRT models have over CTT analyses for this kind of data, since relative weights can be determined for each depressive symptom; more importantly, they are taken into account when calculating the latent trait for each individual. By contrast, when total score is calculated using CTT, all items must be given equal levels of contribution.

Another substantial advantage of IRT models is that they generate Response Category Curves which reveal the association between the levels of intensity of depressive symptoms and the probability that a given category is selected; from such curves, it is possible to determine whether any item has categories that are poorly dimensioned, as occurred in the present study. This finding suggests that individuals responding to BDI cannot distinguish between the assertions defining the response categories for some of the items, demonstrating a need to rethink the measurement scale. Here, this problem occurred in thirteen items, of which two referred to symptoms with very high psychometric information content about the intensity of depressive symptoms namely, pessimism and dissatisfaction. One possible solution is that used in the present work, which was to combine response categories adjacent to the one giving the problem, since it appeared probable that subjects had not been able to distinguish between the information content of assertions in this category.

To establish which items hold more psychometric information about the intensity of depressive symptoms, i.e. those which best discriminate for this latent trait in the population, the point where the item's information function has unit value^16,17 can be taken as a cutoff point, since it is influenced by the magnitude of the slope parameter in the Gradual Response model. In this context, it is interesting to note that, of the seven items that discriminate most efficiently for the latent trait in the population, six performed best in the region where the intensity of depressive symptoms was moderate¹⁵. Only the item associated with self-hatred remained efficient in the region of very intense depressive symptoms region, since its interval on the IRT score was between 1.3 and 2.2, corresponding to an interval 27 to 37 in total score.

Uher et al.¹¹ used other cutoff points for the item slope parameter (a_i) in their study, this being used directly as the item discrimination parameter in the Gradual Response model. These cutoff points divide items into three groups: items giving poor discrimination (a_i < 65); items giving moderate discrimination (0.65 < a_i < 1.34) and items giving good discrimination (a_i > 1.34). Using this criterion, the items giving good discrimination in the present study were sadness, pessimism, feelings of failure, dissatisfaction, and self-hatred (Table 2); except for the last, these items had the same classification as in Uher et al.¹¹ Indecision and work difficulties gave moderate discrimination, as did the majority of items; irritability and weight loss were the only items giving poor discrimination (Table 2).

The 95% percentile of the IRT score, corresponding to a total score of 31, was found to lie in the region of moderately intense depressive symptoms. The group with moderate to heavy depressive symptoms comprises 202 subjects (their IRT scores being not less than the 95% percentile) of which 74% were women, agreeing with previous evidence indicating that depression is two to three times more prevalent in women than in men³¹.

Estimates of the points of intersection b_i,k are divided in two parts; the first, b_i, is the location parameter, and corresponds to a measure of the gravity of the depressive symptom associated with a given BDI item. This allows results to be compared with those given by IRT dichotomous response models, such as models with two or three parameters models (both contain position and slope parameters) when these are used in the same evaluation procedure. Cúri¹⁹ fitted a three-parameter logistic model to BDI data, and found results in moderate agreement with those concerning the severity of depression and discriminatory power of items, reported in the present work, particularly regarding the weight loss item, which is one of the most severe depressive symptoms but which shows poor discrimination (Table 2). Despite this, weight loss information may be extremely relevant for several reasons, for example: it could be a consequence of some clinical condition leading to depression (since there is evidence that depression is strongly associated with chronic pathological conditions such as hypertension, coronary diseases, diabetes, brain hemorrhage, terminal kidney diseases, chronic obstructive pulmonary disease, congenital heart diseases, angina, asthma and arthritis^32-39), or it might be a physical expression of other symptoms such as sadness and tiredness, which might lead to lack of attention to diet, with subsequent weight loss.

There are several advantages of using IRT. In the present study, these are illustrated by the possibility of differentiating and comparing depressive symptoms in terms of their discriminatory power and gravity; by the possibility of associating levels of depressive symptoms with the probability of response to each category, thus showing how well patients understand the scale; by the possibility of comparing the depressive symptoms inferred from each subject with the gravity of each symptom; and others. Even more important is the fact that different weights can be assigned to each item used for estimating the intensity of depressive symptoms (IRT score); this is not possible in CTT models, where subjects with the same total score values are considered identical, even when they responded differently to the questionnaire. This shows up better in Chart 1: nine individuals had a final total score of ten (even though they had different profiles of response to the BDI items) but had different IRT scores, which take account the differences in response profiles to items with different weights when they are calculated (except for Rasch models, in which all items have the same weight in score calculations).

The relevance of IRT models to medical research has already been demonstrated. However, it is important to stress that before such models are used in medical practice, they must be shown to be appropriate for specific populations. Just as the BDI has been used to evaluate the intensity of depressive symptoms, their cutoff points for differentiating between individuals must be determined. Computational development and implementation of IRT models (especially for polytomous response items) which allow for the presence of DFI is also needed, since different groups of subjects often react differently when responding to a given item.

In the BDI, some items demonstrate a sex-differentiated function, in that men and women react differently to them. The fact that the IRT model used in the present work does not allow for the presence of DFI is one potential limitation; another is that the mean age of subjects in the sample is lower than that of the population from which it is drawn, especially for the group not receiving medical treatment.

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Item response theory applied to the Beck Depression Inventory

Stela Maris de Jezus Castro; Clarissa Trentini; João Riboldi

Publication Dates

• Publication in this collection
  13 Sept 2010
• Date of issue
  Sept 2010

History

• Received
  20 July 2009
• Reviewed
  26 June 2010
• Accepted
  12 July 2010