 Research article
 Open Access
 Open Peer Review
 Published:
An evaluation of computerized adaptive testing for general psychological distress: combining GHQ12 and Affectometer2 in an item bank for public mental health research
BMC Medical Research Methodology volume 16, Article number: 58 (2016)
Abstract
Background
Recent developments in psychometric modeling and technology allow pooling wellvalidated items from existing instruments into larger item banks and their deployment through methods of computerized adaptive testing (CAT). Use of item response theorybased bifactor methods and integrative data analysis overcomes barriers in crossinstrument comparison. This paper presents the joint calibration of an item bank for researchers keen to investigate population variations in general psychological distress (GPD).
Methods
Multidimensional item response theory was used on existing health survey data from the Scottish Health Education Population Survey (n = 766) to calibrate an item bank consisting of pooled items from the short common mental disorder screen (GHQ12) and the Affectometer2 (a measure of “general happiness”). Computer simulation was used to evaluate usefulness and efficacy of its adaptive administration.
Results
A bifactor model capturing variation across a continuum of population distress (while controlling for artefacts due to item wording) was supported. The numbers of items for different required reliabilities in adaptive administration demonstrated promising efficacy of the proposed item bank.
Conclusions
Psychometric modeling of the common dimension captured by more than one instrument offers the potential of adaptive testing for GPD using individually sequenced combinations of existing survey items. The potential for linking other item sets with alternative candidate measures of positive mental health is discussed since an optimal item bank may require even more items than these.
Background
Assessment of the psychological component of health via rating scales and questionnaires has a long and continuing history. This is exemplified by the work of Goldberg on his General Health Questionnaire (GHQ) item set(s) [1], but also by many others who have worked on questionnaires measuring “general health” [2]. Goldberg’s GHQ instruments are intended to be scored and used as an assessment of risk for common mental disorder(s) and have become established in health care, help seeking and epidemiological studies including national and crossnational surveys. However, there have also been new and influential measures developed for application in this setting, introduced by researchers from the fields of health promotion, positive psychology, and public (mental) health. Consequently, over the past two decades it has become increasingly common for national and international research studies and health surveys to broaden measurement to a wider range of psychological health concepts in populations [3]. This has resulted in multifaceted definitions and new instrument conventions for fieldwork [4] such that more than one instrument is now likely to be included in health or wellbeing surveys.
Presently, a number of alternative instruments appear popular. Hence there are choices and opportunities for researchers and survey designers to experiment with different assemblies, subsets and orderings of existing items within and across instruments [5–7]. Our impression is that this has been rare to date and therefore several instruments that may all assess a common construct may exist and have been developed in parallel [8]. If this argument holds, then there may be no need to invent or introduce new items or instruments, as existing item sets might be sufficient or adequate, and already complement each other in this regard. If this is the case, they can be combined in order to achieve accurate and efficient measurement of population level variation in public health research.
We suggest that, over the past decade, too much of the debate about the measurement of wellbeing has been about specific instruments, i.e. fixed collections of items, not about the items themselves. Instead of looking at whole instruments and correlations between their scores in order to try to gauge their similarity, the use of item response theory (IRT) based models and joint analysis of items (“cocallibration”) [8–10] may be of greater value in advancing understanding and measurement of psychological distress variation (and dimensions). Such activities make it possible to identify useful items, the extent of overlap between instruments and optimal item sets for specific assessment purposes. Even more than that, IRT models can help to support those who might wish to administer assessments in a shorter time, they offer potentially higher face validity for the individual respondents, yet still with a level of precision that is high enough for any given scientific or practical purpose, as befits any particular study or set of surveys. This can be achieved by employing computeradaptive procedures that do not require researchers to depend on any single specific instrument or measure, but rather to use a broader “pool” of content consisting of a large collection of items calibrated using IRT: a practice that has become known as computerized adaptive testing (CAT) [11]. Since there is potential for most modern surveys to use technologies that allow items to be administered via apps, on mobile devices or through conventional or cloudbased computing platforms, there is no reason why this technology should not be used to its maximum potential, to support adaptive testing ideas in the field of survey research.
In this paper we present such a joint analysis. Our aim is to combine item sets from two instruments (the GHQ12 and Affectometer2) and to offer them as an item bank for general psychological distress [12] measurement. The main aim of such an analysis is the quantification of similarities and overlap across all items  as well as their item parameters  that can be used for further implementation as an “item bank”. Since we will invoke psychometric principles and models that allow for adaptive measurement, we will also emphasize how the measurement error considered under this approach can enhance narratives about lowest permissible measurement precision across individuals.
To this end, we first compared plausible structural models that were derived from the literature for each instrument and then fit an appropriate latent variable model (from the family of IRT models). This approach allowed us to map GHQ12 and Affectometer2 items onto a common dimension measured by both instruments. Hence this general psychological distress "factor" (dimension) was defined via bifactor modeling [13]. Based on this model we next assessed interitem dependencies and the position of the item parameters on the latent continuum to identify which items of the two instruments were possibly exchangeable [14] and would align to one metric.
Building on the previous steps, we then explored the feasibility of administering the joint itemset as a computerized adaptive test drawing on the 52item bank. In the simulation study we took an additional opportunity to compare different estimation procedures and configurations of the CAT algorithms as well as exploring the number of items that are necessary to reliably assess a general psychological distress factor. In doing so we aimed to meet the measurement and practical needs of public mental health researchers.
Methods
Multiitem questionnaires to be jointly calibrated: integrative data analysis approach
Two instruments are introduced as key measures in the dataset chosen for our analysis. We chose instruments for which there is either extensive literature, or interesting items: the former is our justification for using GHQ12, and the latter for including Affectometer2.
The 12  item version of the GHQ is the shortest and probably the most widely used version of the item set originated by Goldberg [15]. GHQ12 was developed as a brief, paper and pencil assessment of psychological distress, indicative of common mental disorder (CMD). It identifies those exceeding a threshold on the sum score – “screen positives” who are at increased risk of a current diagnosis of anxiety and/or depression (i.e. CMD). GHQ12 is best considered as a short form of the GHQ30, which itself comprises half the items in the original GHQ60 [15]. The GHQ30 was intended to be unidimensional and avoided the inclusion of somatic symptoms. Both GHQ30 and GHQ12 contain an equal number of positively and negatively phrased items.
The Affectometer2 is a 40item scale developed in New Zealand to measure general happiness as a sense of wellbeing based on assessing the balance of positive and negative feelings in recent experience [16]. Its items contain both simple adjectives and phrases. The Affectometer2 came to the attention of many UK and international audiences, when it was considered as a starting point for the development of a Scottish population wellbeing indicator. Comparatively little attention had previously been given to the Affectometer2 within the UK (only one publication by Tennant and coauthors [17]). Part of the motivation for our analysis was to understand its items in the context of the latent continuum of population general psychological distress since they developed historically in different contexts and were aimed at different purposes. Our methods allow novel combinations of items to be scored on a single population construct, a latent factor common to the whole set of items, using the widely exploited modeling approach of bifactor IRT [18–20].
Response options, response levels, and scoring
In contrast to the GHQ12, which has four ordinal response levels (for positively worded items: not at all, no more than usual, rather more than usual, much more than usual; for negatively worded items: more than usual, same as usual, less than usual, much less than usual), the Affectometer2 has five ordinal response levels (not at all, occasionally, some of the time, often, all of the time). Some Affectometer2 items, as the instrument has a mixture of positive and negative phrasing, needed to be reversed (half of them) to score in the same “morbidity” direction. Negative GHQ12 items' response levels are already reversed on the paper form and thus their scoring does not need to be reversed. Nonetheless, positive and negative item wording is known to influence responses [13, 21, 22] regardless of reversed scoring of corresponding items. An approach to eliminate this effect is to model its influence as a nuisance (method) factor in factor analysis, for example by using the bifactor model [23] or alternative approaches [24, 25].
Population samples for empirical item analysis
A dataset of complete GHQ12 and Affectometer2 responses was obtained from n = 766 individuals who participated in wave 11 (collected in 2006) of the Health Education Population Survey in Scotland (SHEPS) [26]. This figure comprises effectively half of the total SHEPS sample size that year; the other half was administered the WarwickEdinburgh Mental WellBeing Scale [27]. The long running series of SHEPS in Scotland was started in 1996 and was designed to monitor healthrelated knowledge, attitudes, behaviors and motivations to change in the adult population in Scotland. The questionnaires are administered using computer assisted personal interviewing (CAPI) in respondents' homes.
Development of the latent variable measurement model and item calibration
To empirically test the structural integrity of the 52 items in the proposed general psychological distress item bank we used multidimensional IRT modeling with bifactor principles underpinning our analyses. We tested a priori the hypothesis that both GHQ12 and Affectometer2 items contribute mainly to the measurement of a single dimension (psychological distress). However, apart from this dominant (general) factor, responses might also be influenced by methodological features such as item wording (as noted earlier half of the items in the GHQ12 and Affectometer2 are positively worded and half negatively worded).
Several approaches have been suggested to model variance specific to methods factors [24, 25]. To accommodate the possible influences of such item wording effects when seeking the relevant estimates for the main construct of general psychological distress (GPD) we elected to apply a socalled M1 model [25]. This model assumes the existence of a general factor as well as M1 method latent variables where M stands for specific (nuisance) factors explaining the common variance of items sharing the same wording. In the framework of our study, the M1 model translates into the general factor accounting for shared variance (here GPD) across all 52 items in our item bank and one specific factor accounting for positively worded items from both measures^{Footnote 1}. Figure 1 provides a graphical representation of the M1 model.
To demonstrate the relevance of a bifactor approach for our data, we compare its fit to data with a unidimensional solution, i.e. a solution where all items load on a general factor and no specific factors are included. For evaluation of model fit, traditional fit indices were used, including SatorraBentler scaled chisquare [28], comparative fit index (CFI) [29], TuckerLewis fit index (TLI) [30] and root mean square error of approximation (RMSEA) [31]. Corrected χ^{2} difference test was used for the comparison [32]. All models were estimated with MPlus [33] using mean and variance adjusted Weighted Least Squares (WLSMV) estimation. Therefore the resulting model can be referred as the normal ogive Graded Response Model (GRM) [34, 35].
CAT simulation
Before the simulation of the adaptive administration of this item bank could be carried out, the factor analytic estimates needed to be converted to IRT parameters by using the following formulas [18, 36]; for each item i = 1, … P influenced by m = 1,…,M factors, the discrimination (α_{ im }) and k IRT thresholds (t_{ ik }) on item i are
\( {\alpha}_{im}=\frac{1.7\times {\lambda}_{im}}{\sqrt{1{\displaystyle \sum_{m=1}^M{\lambda}_{im}^2}}} \) and \( {t}_{ik}=\frac{1.7\times {\tau}_{ik}}{\sqrt{1{\displaystyle \sum_{m=1}^M{\lambda}_{im}^2}}} \),
where λ_{ im } is factor loading of the item on factor m, τ_{ ik } are the corresponding item thresholds and the scaling constant 1.7 converts estimates from the normal ogive metric of the factor model into logistic IRT metric needed for the CAT application.
To evaluate the performance of the proposed item bank we set up a Monte Carlo simulation. The simulation can be used to evaluate the efficacy of CAT administration and also the proximity of the latent factor values from the CAT administration (θ_{ est }) to the true latent factor values (θ_{ true }). In such a setting, a matrix of item parameter estimates from a calibration study and a vector of values of θ_{ true } need to be provided. Also, the IRT model has to be specified. The process can be outlined as follows:

1.
Simulate latent factor values from the desired distribution (θ_{ true }) which serve as “true” latent distress values of the simulated respondents.
For the purposes of our simulation we first simulated 10,000 θ_{ true } values from standard normal distribution N(0,1) which is the presumed empirical distribution of distress in the general population. These values are therefore used to investigate the functioning of the item bank in its epidemiological context. We also ran a second simulation based on 10,000 θ_{ true } values drawn from uniform distribution U(3,3). Although such a distribution of distress is unlikely in the general population, the rationale is to eliminate the influence of the empirical distribution of the latent factor on CAT performance.

2.
Supply item parameter estimates and choose the corresponding IRT model.
In the context of our study, this step means to supply IRT parameters (discriminations and item thresholds) from item calibration and define which model was used for the calibration (normal ogive GRM in our case). Together with the θ_{ true } values simulated from the previous step, this provides the information needed for a simulated CAT administration, because stochastic responses to the items can be generated (see step 4).

3.
Set CAT administration options
This step involves the selection of a latent factor estimation method, item selection method, termination criteria and other CAT specific settings. It requires careful selection of manipulated options since otherwise the number of cells in the simulation design increases rapidly. In our simulation, we aimed to evaluate the performance of the item bank in combination with the following:

Latent factor (θ) estimators [37]:

a.
Maximum likelihood estimation (MLE)

b.
Bayesian modal estimation (BME)

c.
Expected A Priori estimation (EAP).

a.

Item selection methods:
For more details about implementation of these algorithms please see [41]

Priors for the distribution of θ in the population (only for BME and EAP):

a.
(standard) normal

b.
uniform.

a.

Termination criteria (whichever comes first): a) standard error of measurement thresholds: 0.25; 0.32; 0.40, 0.45, 0.50 or b) all items are administered.
This resulted in the 50 cells in the simulation design matrix. The following settings were kept constant across all cells:

Initial θ starting values: random draws from U(1,1)

Number of items selected for starting portion of CAT: 3

Number of the most informative items from which the function randomly selects the next item of CAT: 1 (i.e. the most informative item is always selected).
Additional parameters can be added to control the frequency of item selection (indeed most informative items tend to be selected too often and the least informative are selected rarely – this issue is known as item exposure). We do not control for item exposure in our study as it is not considered (yet) to be of great concern in mental health assessment applications, but the simulation study also allowed us to explore the relevance of this aspect for this item bank.

4.
Simulate CAT administration
Within each of the cells of the simulation design, an administration of the item bank is simulated for each randomly generated θ_{ true } value (from step 1). Based on an initial starting θ value, three items are chosen from the item bank (see step 3, initial θ starting values) and stochastic responses are calculated for the respective θ_{ true } values. Based on these responses, an initial estimate of the latent factor value is calculated (see step 3, θ estimators); for which a new item to present is selected from the item bank (see step 3, item selection methods). This process is repeated until a preset termination criterion is reached (see step 3, termination criteria). This process mimics standard CAT applications [11] and results in estimates (θ_{ est }) for each of the simulated θ_{ true }.
The CAT simulation analysis was performed in the R package catIrt [41]. Please consult its reference manual [41] for a full description of available simulation options. Key information was stored for each simulated CAT administration: which items were administered and their order, estimated θ_{est} and its standard error after item administration. Computer code is provided in an Additional file 1.
CAT performance was assessed by means of the number of administered items, mixing of items from GHQ12 and Affectometer2 during CAT administration, and by the proximity of θ_{ est } from CAT administration to the simulated θ_{ true }. Such proximity can be evaluated based on the root mean squared error, computed as
\( RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum {\left({\theta}_{est}{\theta}_{true}\right)}^2}} \).
Thus, values can be interpreted as the standard deviation of the differences (on the logit scale) between the CAT estimated and the true θs. We also present correlations between these two quantities. Lower values of RMSE and correlations closer to unity indicate better performance.
Results
The left half of Table 1 presents factor loadings and thresholds of the M1 model. Although χ^{2} indicates significant misfit (χ^{2} = 4653, df = 1248, p < 0.001), other fit indices indicate marginal fit (CFI = 0.922; TLI = 0.917, RMSEA = 0.063). This model showed significant improvement in model fit when compared to the unidimensional solution (χ^{2} difference = 948, df = 26, p < 0.001).
Contrary to what we expected based on the literature, the GHQ12 positive items did not load on the positive factor (all items show low negative loadings) suggesting that positive items from both instruments do not have much shared variance after accounting for the general factor. Therefore, the updated model considered positively worded items from GHQ12 and Affectometer2 (posGHQ and posAff factors respectively) to be separate but correlated factors. The fit to data of this updated model was better compared to the M1 model (χ^{2} = 3135, df = 1247, p < 0.001; CFI = 0.957; TLI = 0.954, RMSEA = 0.047), and direct comparison of both models revealed significant improvement over the M1 model (χ^{2} difference = 321, df = 1, p < 0.001). This model was statistically better motivated given the high loadings for the positively worded GHQ12 items (on the corresponding specific factor). Finally, this model showed better fit in comparison to the unidimensional model (χ^{2} difference = 1320, df = 27, p < 0.001). Factor loadings and thresholds are presented in the right half of Table 1.
The correlation between the two factors accounting for positively worded items was statistically significant (p = 0.003) though small (0.143) suggesting relative independence of the positive wording method factors in GHQ12 and Affectometer2. Item loadings for both measures on the general factor were, with the exception of Affectometer2 item “Interested in others” (Aff 26), all larger than 0.4 which has been suggested as a reasonable cutoff value [42]. This suggests that all covariances of items in our item bank could be explained to a reasonable extent by the single latent factor hypothesized as a population continuum of “general psychological distress”. This interpretation is supported by an ω_{H} = .90, which indicates that responses are dominated by this single general factor [18, 36, 43].
After the joint calibration on the general factor, it is possible to compare the conditional standard error of measurement (SEM) for the general factor when using either all items or specific subsets of items from the item bank. The comparison of measurement errors of individual instruments revealed that both the GHQ12 and the Affectometer2 were best suited to assess more distressed states: Factor estimates above the population mean (“0” in Fig. 2, i.e. more distressed individuals), were associated with a lower standard error of measurement and thus more precisely assessed. The difference between these two item sets was mainly due to their differences in test length as well as the number of response categories (both favour the Affectometer2). Figure 2 also shows the conditional measurement error for those 12 items from the 52item bank that are optimally targeted at each distress level to explore whether the item bank improves upon the GHQ12. In steps of 0.15 along the GPD continuum (xaxis) those 12 items with the highest information function for each specific distress level were selected and their joint information I(θ) was converted into the conditional measurement error (\( 1/\sqrt{I\left(\theta \right)} \)). The resulting conditional standard error is presented as the dashdotted line and it illustrates the gain in measurement precision by using items from more than one instrument: in the slightly artificial case of having to choose an optimal 12 item version it is neither the widely reliedupon item set of the GHQ12 that is chosen, nor is it only Affectometer2 items with more response categories. Instead, this scenario already illustrates that different items can be of different value for specific assessment purposes and levels of distress. In the following simulation study we assessed this question more generally as well as methodological questions comparing different selection and estimation algorithms for adaptive situations.
The solid line in Fig. 2 shows measurement error along distress levels of the combined instruments. It can also be viewed as a justification for our most stringent termination criteria with respect to SEM in our simulation (see Methods section): SEM values below 0.25 cannot be achieved with this item bank and therefore it makes little sense to include them in the simulation.
Transformation of factor analytic estimates into relevant IRT parameters
For the final model considered in our item bank, negative items load on the general factor (distress) only but positive items load on both the general as well as one of the method factor (posGHQ and posAff respectively). Therefore, the number of dimensions for negative items is M = 1 but for positive items M = 2. As noted previously, to eliminate the influence of item wording, we considered and converted IRT estimates only for the general factor in this model (CAT algorithms for item banks where specific factors are deemed to add further substantive information appear elsewhere [44]). Converted IRT estimates of the items included in our bank are presented in Table 2.
CAT simulation
We used IRT parameters from Table 2 and a vector of 10,000 values of θ_{ true } sampled from the standard normal and uniform distributions as an input for our simulation. We then manipulated (1) θ estimator, (2) item selection method, (3) termination criteria and (4) prior information on distress distribution in the population (for BME and EAP estimators).
To evaluate the efficacy of CAT administration we present the number of administered items needed to reach >the desired termination criteria in Table 3. The results indicate that, to reach a high measurement precision [45, 46] of the score (i.e. standard error of measurement (SEM) = 0.25), 23–30 items on average need to be administered regardless of θ estimator, item selection method, or θ_{ true } distribution. Not surprisingly, the number of items needed decreases dramatically as the desired SEM cutoff increases (and thus measurement precision decreases). For example, when the desired SEM cutoff is 0.32, CAT administration requires on average 10–15 items; and only 4–7 items are required for a SEM cutoff of 0.45. It is not surprising that maximum likelihoodbased and Bayesian θ estimators with noninformative (uniform) priors are similarly effective since they are formally equivalent. However, the normal prior helps to further decrease the number of administered items, even for uniformly distributed θ_{ true } values. Informationbased and KullbackLeibler item selection algorithms are similarly effective.
Table 4 shows the mixing of items from both GHQ12 and Affectometer2 when jointly used for CAT administration. Such mixing is relatively stable across all scenarios for high measurement precisions. The variability across scenarios increases with decreasing demands for measurement precision. Note, that the percentage of GHQ12 items within the item bank was 23.1 %. We emphasize that neither item exposure control nor content balancing was used in our simulations.
Values of RMSE between final θ estimates from CAT administration (θ_{ est }) and their corresponding values of θ_{ true } are provided in Table 5.
Results show that the square root of mean square deviations between the true and estimated θ values lies between 0.247 and 0.619 logit (i.e. between 0.15 and 0.36 standard deviation).
Another traditional approach for evaluating the proximity of the estimated and true θs is the correlation coefficient. Figure 3 therefore provides scatterplots of θ_{ true } on the xaxis and the final estimates θ_{ est } from the CAT administration on the yaxis (for the UWFI method of item selection).
The red line represents perfect correlation between θ_{ true } and θ_{ est }, the blue one shows the fitted regression line. Figure 3 also shows no systematic bias of CAT estimated θs for all SEM cutoffs (dots are distributed symmetrically along the red line). As expected, correlation is lower as the measurement precision decreases, though it is still around 0.9 even for a SEM cutoff of 0.50.
Discussion
The development of an item bank for measurement of psychological distress is a timely challenge amid public mental health debates over measuring happiness /wellbeing or depression [47–51]. In this paper we have presented, to our knowledge, the first calibration of items to measure GPD “adaptively” focusing on practical issues in the transition from multiinstrument paper and pencil assessments to modern adaptive ones based on item banks created from existing validated items. We chose the GHQ12 and the Affectometer2 because they are close in terms of content, and target population [16] but were derived differently. We have demonstrated that their items measure a common dimension, which is in keeping with others’ prior notions of general psychological distress. Potentially more instruments targeting the same or similar constructs can be combined to develop large item banks desirable for adaptive testing. Thus, we do not necessarily need to invent new instruments or items  we can instead combine existing and validated ones^{Footnote 2}.
Importantly, the combination of both instruments leads to an item bank which is more efficient than using either instrument on its own. Compared to the GHQ12, using the same number of items results in a higher measurement precision (dashdotted line in Fig. 2) and compared to the Affectometer2 a smaller number of items will result in sufficient measurement precision for a broad range of distress levels and assessment applications. In addition, although the Affectometer2 already consists of 40 items, the simulation study (Table 4) shows that the GHQ12 complements its coverage of the latent construct. These can be seen as considerable advantages over the traditional use of single instruments.
Pooling and calibration of this relatively small set of items required subtle analytic considerations regarding positive wording of items present in both GHQ12 and Affectometer2. To eliminate the influence of wording effects on our general factor we used the M1 modelling approach [25]. A model with a single method factor accounting for the positive wording used by items in both measures was compared to an alternative model with separate method factors for positively worded items in the GHQ12 and Affectometer2. Low method factor loadings of GHQ12 items and only marginal fit of the former model suggest the superiority of the latter model. Interestingly, results show the positive factors from each measure to be relatively independent.
A large literature has considered the potential multidimensionality of the GHQ12 [52–54]. Usually two correlated factors, one for positive and one for negative items, have been reported. Some authors have interpreted this finding as evidence for the GHQ12 measuring positive and negative mental health. Others have voiced the concern that the second factor is mostly a methods artifact [55] due to item wording. Our item response theory based factor analysis suggests that it probably is not the former, because if the items of the GHQ12 and the Affectometer2 were designed to assess positive mental health with the positively phrased items and mental distress with the negatively phrased ones, then this should be mirrored by a twofactor solution across both instruments. Instead, in our models, GHQ12 and Affectometer2 need separate method factors to explain leftover variance in the positively phrased items. This suggests that there is little support for either the same response tendency or the same latent construct underlying the positively worded items across both instruments. This is an important finding, since it indicates first that both instruments, across all their items, assess a single dimension and secondly, that the additional variance in the positively phrased items needs at least two relatively uncorrelated variables as an adequate explanatory model. There is of course interest in exactly what these factors capture, but this is difficult to say without external validation data [8]. It could be, for example, that one of them actually is a pure methods factor, while the other captures a component of positive affect [56, 57]. How relevant this latter question is, remains to be seen, since our results improve further on the current state of this debate: A reliability estimate of ω_{H} = .90 for the general psychological distress factor highlights that the systematic variance connected with the positively phrased items of both instruments comprises only a marginal proportion of the total variance in responses.
Most importantly for our purposes here, it is the factor loadings on the general factor from a model with separate method factors for positively worded items that were transformed into IRT parameters to calibrate our general psychological distress (GPD) continuum. These were then used as input for our simulation of the efficacy of CAT administration of this candidate item bank. Depending on the combination of θ estimator and item selection method, the average number of items required for CAT administration to reach a SEM cutoff of 0.32 typically required for studies using individual level assessment ranged from 10 to 15. The number of administered items can be further reduced if lower precision is acceptable (see Table 3). These figures show evidence of high efficiency and therefore the usefulness of CAT administration to reduce burden on respondents. However, these results have to be judged within the CAT context and they do not provide information on the number of items needed for a selfreport approach to distress assessment with traditional fixedlength questionnaires. The CAT application uses a set of different questions for each respondent optimized for their respective distress levels. Fixedformat questionnaires do not have this flexibility and unless they are targeted at a specific factor level, they probably need to be (much) longer than the results of the CAT simulation indicate [12, 58].
In our simulation we selected frequently used options to show how different combinations of CAT settings may affect the number of administered items. In terms of efficacy, the results suggest rather similar performance of most of them. However, an informative (standard normal) prior helps to further reduce the number of items, especially for lower measurement precisions. Researchers should be cautious when specifying informative priors though, as priors not corresponding with the population distribution may have an adverse effect on the number of administered items [59].
We believe that our argument and technical work are illustrative and compelling as a justification for future fieldwork. However, there are clearly some limitations of our study. It is important to recognize that the simulation may show slightly overoptimistic results in terms of CAT efficiency. This is because the idealized persons’ responses to items during our CAT simulation are based on modelled probabilities and thus follow precisely the item response model used for calibration. Thus the extent of model misfit from the empirical samples is not taken into account by this work. When items are calibrated using a very large sample of respondents, this is not a big issue, but our calibration sample was of only a moderate size and therefore our item bank may need recalibration in larger empirical datasets. We are not aware of any existing large dataset that allows this, but it could become a priority to explore such a dataset.
An aspect important for future content development is the GPD factor itself. Here, we offer this term over the original terminology (“common mental disorder”) frequently associated with the GHQ because our item bank includes Affectometer2 items and therefore the measured construct is broader. Looking at the items that have been used in the past, approaches to measure GPD currently range from symptoms of mental disorders, a perspective which overlaps with the GHQ12 tradition [60–62], to definitions based on the affective evaluation, closer to the underlying rationale of the Affectometer2 [56, 57]. These, sometimes more deficit oriented perspectives can then be contrasted with similar assessments based on positive psychology or wellbeing theories [27, 63]. The interrelations of these frameworks are currently underresearched and more integrative research on these is needed [8, 64, 65]. It should be noted that while our analysis presents evidence for overlap between two of these positions, this does not cover all relevant frameworks, nor do we present evidence for predictive or differential validity of the item sets, which would have been beyond the scope of this work.
Conclusions
The CAT administration of the proposed item bank consisting of GHQ12 and Affectometer2 items is more efficient than the use of either measure alone and its use shows a reasonable mixing of items from each of the two measures. The approach outlined in this manuscript combines previous work on data integration and multidimensional IRT, and together with other important and similarly minded developments in the field [66–68] illustrates a possible future of quick and broad assessments in epidemiology and public mental health.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Availability of data and materials
Data from these secondary data analyses of the SHEPS sample were supplied by the UK Data Archive (study number SN5713) and can be accessed at https://discover.ukdataservice.ac.uk.
Notes
 1.
The selection of modelling a specific factor for negatively or positively worded items is arbitrary and depends on the selection of “reference wording”. We selected the negative wording as our reference type of wording.
 2.
Subject to considerations regarding copyright permissions.
Abbreviations
 BME:

bayesian modal estimation
 CAPI:

computer assisted personal interviewing
 CAT:

computerized adaptive testing
 CFI:

comparative fit index
 CMD:

common mental disorder
 EAP:

Expected A Priori
 FPKL:

pointwise KullbackLeibler divergence
 GHQ:

General Health Questionnaire
 GPD:

general psychological distress
 GRM:

graded response model
 IRT:

item response theory
 MLE:

maximum likelihood estimation
 RMSE:

root mean squared error
 RMSEA:

root mean square error of approximation
 SEM:

standard error of measurement
 SHEPS:

Scottish Health Education Population Survey
 TLI:

TuckerLewis index
 UWFI:

unweighted Fisher information
 WLSMV:

mean and variance adjusted Weighted Least Squares
References
 1.
Goldberg DP, Williams P. A user's guide to the General Health Questionnaire. Windsor UK: NFERNelson; 1988.
 2.
McDowell I. Measuring health: A guide to rating scales and questionnaires. New York: Oxford University Press; 2006.
 3.
StewartBrown S. Defining and measuring mental health and wellbeing. In: Knifton L, Quinn N, editors. Public mental health: global perspectives. edn. New York: McGraw Hill Open University Press; 2013. p. 33–42.
 4.
Lindert J, Bain PA, Kubzansky LD, Stein C. Wellbeing measurement and the WHO health policy Health 2010: systematic review of measurement scales. Eur J Public Health. 2015;25(4):731–40.
 5.
Wahl I, Löwe B, Bjorner JB, Fischer F, Langs G, Voderholzer U, Aita SA, Bergemann N, Brähler E, Rose M. Standardization of depression measurement: a common metric was developed for 11 selfreport depression measures. J Clin Epidemiol. 2014;67(1):73–86
 6.
Weich S, Brugha T, King M, McManus S, Bebbington P, Jenkins R, Cooper C, McBride O, StewartBrown S. Mental wellbeing and mental illness: findings from the Adult Psychiatric Morbidity Survey for England 2007. Br J Psychiatry. 2011;199(1):23–8.
 7.
Gibbons RD, Perraillon MC, Kim JB. Item response theory approaches to harmonization and research synthesis. Health Serv Outcomes Res Methodol. 2014;14(4):213–31.
 8.
Böhnke JR, Croudace TJ. Calibrating wellbeing, quality of life and common mental disorder items: psychometric epidemiology in public mental health research. Br J Psychiatry. 2015. doi:10.1192/bjp.bp.115.165530.
 9.
Hussong AM, Curran PJ, Bauer DJ. Integrative data analysis in clinical psychology research. Annu Rev Clin Psychol. 2013;9:61–89.
 10.
Bauer DJ, Hussong AM. Psychometric approaches for developing commensurate measures across independent studies: traditional and new models. Psychol Methods. 2009;14(2):101–25.
 11.
Wainer H, Dorans NJ, Flaugher R, Green BF, Mislevy RJ. Computerized adaptive testing: A primer. Hillsdale, NJ: Lawrence Erlbaum; 2000.
 12.
Böhnke JR, Lutz W. Using item and test information to optimize targeted assessments of psychological distress. Assessment. 2014;21(6):679–93.
 13.
Hankins M. The factor structure of the twelve item General Health Questionnaire (GHQ12): The result of negative phrasing? Clin Pract Epidemiol Ment Health. 2008;4(1):10.
 14.
Egberink IJL, Meijer RR. An item response theory analysis of Harter’s SelfPerception Profile for children or why strong clinical scales should be distrusted. Assessment. 2011;18(2):201–12.
 15.
Goldberg DP. The detection of psychiatric illness by questionnaire. London: Oxford University Press; 1972.
 16.
Kammann R, Flett R. Affectometer 2: A scale to measure current level of general happiness. Aust J Psychol. 1983;35(2):259–65.
 17.
Tennant R, Joseph S, StewartBrown S. The Affectometer 2: a measure of positive mental health in UK populations. Qual Life Res. 2007;16(4):687–95.
 18.
Reise SP. The rediscovery of bifactor measurement models. Multivar Behav Res. 2012;47(5):667–96.
 19.
Gibbons RD, Bock RD, Hedeker D, Weiss DJ, Segawa E, Bhaumik DK, Kupfer DJ, Frank E, Grochocinski VJ, Stover A. FullInformation item bifactor analysis of graded response data. Appl Psych Meas. 2007;31(1):4–19.
 20.
Gibbons R, Hedeker D. Fullinformation item bifactor analysis. Psychometrika. 1992;57(3):423–36.
 21.
Romppel M, Braehler E, Roth M, Glaesmer H. What is the General Health Questionnaire12 assessing?: Dimensionality and psychometric properties of the General Health Questionnaire12 in a large scale German population sample. Compr Psychiatry. 2013;54(4):406–13.
 22.
Ye S. Factor structure of the General Health Questionnaire (GHQ12): The role of wording effects. Pers Indiv Differ. 2009;46(2):197–201.
 23.
Wang WC, Chen HF, Jin KY. Item response theory models for wording effects in mixedformat scales. Educ Psychol Meas. 2014;75(1):15778.
 24.
Pohl S, Steyer R. Modeling common traits and method effects in multitraitmultimethod analysis. Multivar Behav Res. 2010;45(1):45–72.
 25.
Geiser C, Lockhart G. A comparison of four approaches to account for method effects in latent state–trait analyses. Psychol Methods. 2012;17(2):255–83.
 26.
Scotland NH. Health Education Population Survey. Colchester, Essex: UK Data Archive; 2006.
 27.
Tennant R, Hiller L, Fishwick R, Platt S, Joseph S, Weich S, Parkinson J, Secker J, StewartBrown S. The WarwickEdinburgh Mental Wellbeing Scale (WEMWBS): development and UK validation. Health Qual Life Outcomes. 2007;5:63.
 28.
Satorra A, Bentler PM. Corrections to test statistics and standard errors in covariance structure analysis. In: von Eye A, Clogg CC, editors. Latent variables analysis: Applications for developmental research. edn. Thousand Oaks: Sage; 1994. p. 399–419.
 29.
Bentler PM. Comparative fit indexes in structural models. Psychol Bull. 1990;107:238–46.
 30.
Tucker LR, Lewis C. A reliability coeffficient for maximum likelihood factor analysis. Psychometrika. 1973;38:1–10.
 31.
Steiger JH, Lind J. Statisticallybased tests for the number of common factors. Paper presented at the annual Spring Meeting of the Psychometric Society in Iowa City. May 30, 1980.
 32.
Satorra A. Scaled and adjusted restricted tests in multisample analysis of moment structures. In: Heijmans RDH, Pollock DSG, Satorra A, editors. Innovations in multivariate statistical analysis A Festschrift for Heinz Neudecker. edn. London: Kluwer Academic Publishers; 2000. p. 233–47.
 33.
Muthén L, Muthén B. Mplus: Statistical analysis with latent variables. Version 7.3. Los Angeles, CA: Muthén & Muthén; 19982016.
 34.
Samejima F. Estimation of latent ability using a response pattern of graded scores, Psychometric Monograph no 17. 1969.
 35.
Takane Y, Leeuw J. On the relationships between item response theory and factor analysis of discretized variables. Psychometrika. 1987;52(3):393–408.
 36.
McDonald RP. Test theory: A unified treatment. Mahwah: Lawrence Erlbaum Associates, Inc.; 1999.
 37.
Baker FB, Kim SH. Item response theory: Parameter estimation techniques. New York: Marcell Dekker; 2004.
 38.
Veerkamp WJ, Berger MP. Some new item selection criteria for adaptive testing. J Educ Behav Stat. 1997;22(2):203–26.
 39.
van der Linden W. Bayesian item selection criteria for adaptive testing. Psychometrika. 1998;63(2):201–16.
 40.
Chang HH, Ying Z. A global information approach to computerized adaptive testing. Appl Psych Meas. 1996;20(3):213–29.
 41.
Nydick SW: catIrt: An R package for simulating IRTbased computerized adaptive tests. R package version 0.42. http://CRAN.Rproject.org/package=catIrt. In.; 2014.
 42.
Fliege H, Becker J, Walter OB, Bjorner JB, Klapp BF, Rose M. Development of a computeradaptive test for depression (DCAT). Qual Life Res. 2005;14(10):2277–91.
 43.
Zinbarg R, Revelle W, Yovel I, Li W. Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their relations with each other and two alternative conceptualizations of reliability. Psychometrika. 2005;70(1):123–33.
 44.
Weiss DJ, Gibbons RD. Computerized adaptive testing with the bifactor model. In: Proceedings of the 2007 GMAC Conference on Computerized Adaptive Testing: 2007. 2007.
 45.
Dimitrov DM. Marginal truescore measures and reliability for binary items as a function of their IRT parameters. Appl Psych Meas. 2003;27(6):440–58.
 46.
Green BF, Bock RD, Humphreys LG, Linn RL, Reckase MD. Technical guidelines for assessing computerized adaptive tests. J Educ Meas. 1984;21(4):347–60.
 47.
Seligman ME, Steen TA, Park N, Peterson C. Positive psychology progress: empirical validation of interventions. Am Psychol. 2005;60(5):410–21.
 48.
Ryff CD. Happiness is everything, or is it? Explorations on the meaning of psychological wellbeing. J Pers Soc Psychol. 1989;57(6):1069.
 49.
Wood AM, Taylor PJ, Joseph S. Does the CESD measure a continuum from depression to happiness? Comparing substantive and artifactual models. Psychiatry Res. 2010;177(1):120–3.
 50.
Joseph S, Lewis CA. The Depression–Happiness Scale: Reliability and validity of a bipolar self‐report scale. J Clin Psychol. 1998;54(4):537–44.
 51.
Kammann R, Farry M, Herbison P. The analysis and measurement of happiness as a sense of wellbeing. Soc Indic Res. 1984;15(2):91–115.
 52.
Shevlin M, Adamson G. Alternative factor models and factorial invariance of the GHQ12: a large sample analysis using confirmatory factor analysis. Psychol Assess. 2005;17(2):231–6.
 53.
Werneke U, Goldberg DP, Yalcin I, Ustun BT. The stability of the factor structure of the General Health Questionnaire. Psychol Med. 2000;30(4):823–9.
 54.
Hu Y, StewartBrown S, Twigg L, Weich S. Can the 12item General Health Questionnaire be used to measure positive mental health? Psychol Med. 2007;37(7):1005–13.
 55.
Molina JG, Rodrigo MF, Losilla JM, Vives J. Wording effects and the factor structure of the 12item General Health Questionnaire (GHQ12). Psychol Assess. 2014;26(3):1031–7.
 56.
Crawford JR, Henry JD. The positive and negative affect schedule (PANAS): construct validity, measurement properties and normative data in a large nonclinical sample. Br J Clin Psychol. 2004;43(Pt 3):245–65.
 57.
Simms LJ, Gros DF, Watson D, O’Hara MW. Parsing the general and specific components of depression and anxiety with bifactor modeling. Depress Anxiety. 2008;25(7):E34–46.
 58.
Emons WHM, Sijtsma K, Meijer RR. On the consistency of individual classification using short scales. Psychol Methods. 2007;12(1):105–20.
 59.
van der Linden WJ, Glas CAW, editors. Elements of adaptive testing. New York: Springer; 2010.
 60.
Urban R, Kun B, Farkas J, Paksi B, Kokonyei G, Unoka Z, Felvinczi K, Olah A, Demetrovics Z. Bifactor structural model of symptom checklists: SCL90R and Brief Symptom Inventory (BSI) in a nonclinical community sample. Psychiatry Res. 2014;216(1):146–54.
 61.
Glaesmer H, Braehler E, Grande G, Hinz A, Petermann F, Romppel M. The German version of the Hopkins Symptoms Checklist25 (HSCL25): Factorial structure, psychometric properties, and populationbased norms. Compr Psychiatry. 2014;55(2):396–403.
 62.
Stochl J, Khandaker GM, Lewis G, Perez J, Goodyer IM, Zammit S, Sullivan S, Croudace TJ, Jones PB. Mood, anxiety and psychotic phenomena measure a common psychopathological factor. Psychol Med. 2015;45(07):1483–93.
 63.
Jovanović V. Structural validity of the Mental Health ContinuumShort Form: The bifactor model of emotional, social and psychological wellbeing. Pers Indiv Differ. 2015;75:154–9.
 64.
Camfield L, Skevington SM. On subjective wellbeing and quality of life. J Health Psychol. 2008;13(6):764–75.
 65.
Wood AM, Tarrier N. Positive Clinical Psychology: a new vision and strategy for integrated research and practice. Clin Psychol Rev. 2010;30(7):819–29.
 66.
Gibbons RD, Weiss DJ, Pilkonis PA, Frank E, Moore T, Kim JB, Kupfer DJ. Development of a computerized adaptive test for depression. Arch Gen Psychiatry. 2012;69(11):1104–12.
 67.
Gibbons RD, Weiss DJ, Kupfer DJ, Frank E, Fagiolini A, Grochocinski VJ, Bhaumik DK, Stover A, Bock RD, Immekus JC. Using computerized adaptive testing to reduce the burden of mental health assessment. Psych Serv. 2008;59(4):361–8.
 68.
Gibbons RD, Weiss DJ, Pilkonis PA, Frank E, Moore T, Kim JB, Kupfer DJ. Development of the CATANX: a computerized adaptive test for anxiety. Am J Psychiatry. 2014;171(2):187–94.
Acknowledgements
Not applicable.
Funding
This work was conducted whilst JS was funded by the Medical Research Council (MRC award reference MR/K006665/1), partly also by Charles University PRVOUK programme nr. P38. JS was supported by NIHR CLAHRC East of England.
Author information
Additional information
Competing interest
TJC reports grants from GL Assessment (20082011) held whilst at the University of Cambridge (with Prof J Rust) for an ability test standardization project. TJC and JS report a personal fee from GL Assessment for psychometric calibration of the BAS3 (ability tests) outside the submitted work. GL Assessment sell the General Health Questionnaire.
JB and KP declare that they have no competing interests.
Authors’ contributions
Analysis and interpretation of data, drafting and revision of the article – JS; drafting and revision of the article  JRB; revision of the article  KP; drafting and revision of the article, suggestion to jointly calibrate GHQ12 and Affectometer2 as an item bank – TJC; critical revision for important intellectual content – all authors. All authors read and approved the final manuscript.
Additional file
Additional file 1:
R code for CAT simulation (DOCX 23.7 kb)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
About this article
Received
Accepted
Published
DOI
Keywords
 Computerized adaptive testing
 General Health Questionnaire
 Affectometer
 Item Response Theory