Introduction

The distinction between fluid (Gf) and crystallized intelligence (Gc), first made by Horn and Cattell (Reference Horn and Cattell1), has proven to be useful in neuropsychological assessment (Reference Kaufman, Lichtenberger and Kaufman2). Gf is the ability to solve novel problems by using reasoning, and Gc is a knowledge-based ability that depends on schooling and acculturation (Reference Horn and Cattell1,Reference Kaufman, Kaufman and Plucker3). Gf and Gc have different functional properties. For instance, fluid abilities tend to decline from the age of 20, whereas Gc stays relatively preserved during ageing. Moreover, Gf is sensitive to brain damage, while Gc typically shows minor impairment after brain lesions (Reference Kaufman, Kaufman and Plucker3). Examining general intelligence (g), fluid tests consistently appear to be its best predictors (Reference Roca, Manes and Cetkovich4).

Executive functioning (EF) is a complex concept and beholds multiple cognitive processes which are responsible for controlling and regulating thoughts, emotions, and behaviour and enable us to adjust to new situations (Reference Diamond5–Reference Miyake, Friedman, Emerson, Witzki and Howerter7). Miyake et al. (Reference Miyake, Friedman, Emerson, Witzki and Howerter7) identified updating, inhibition, and shifting as separate building blocks of EF, which together are a prerequisite for complex behaviour or ‘higher-level executive functions’ (Reference Diamond5). On the contrary, the unitary nature of EF becomes apparent in, for instance, the supervisory attentional system (SAS) by Norman and Shallice (Reference Norman and Shallice10). Being a contention scheduling based monitoring programme, SAS selects sets of actions competing for representation and would thus be responsible for executive control of complex, goal-oriented behaviour. In recent years, researchers seemed to agree upon the approach that EF can be conceptualised as a unitary construct as well as consisting of diverse functions (Reference Friedman, Miyake, Corley, Young, DeFries and Hewitt8,Reference McCabe, Roediger, McDaniel, Balota and Hambrick9).

Duncan et al. demonstrated that Gf is sensitive to frontal lobe lesions, leading to the conclusion that Gf is in fact a reflection of EF (Reference Duncan, Burgess and Emslie11). Evidence from functional imaging studies further corroborates this overlap between Gf and EF in patients with frontal lobe lesions (Reference Barbey, Colom, Paul and Grafman12–Reference Woolgar, Parr and Cusack14), Parkinson’s disease (Reference Roca, Manes and Chade15), fronto-temporal dementia (Reference Roca, Manes and Gleichgerrcht16) and schizophrenia (Reference Roca, Manes and Cetkovich4). In subsequent years, an increasing amount of studies addressed the Gf–EF relation (Reference Miyake, Friedman, Emerson, Witzki and Howerter7–Reference McCabe, Roediger, McDaniel, Balota and Hambrick9,Reference Salthouse and Pink17–Reference Salthouse and Davis19). In general, Gf seems to correlate highly with working memory, whereas other aspects of EF (inhibition, mental set-shifting) usually show less strong relations with Gf (Reference Miyake, Friedman, Emerson, Witzki and Howerter7,Reference Friedman, Miyake, Corley, Young, DeFries and Hewitt8,Reference Salthouse, Atkinson and Berish18–Reference Unterrainer, Rahm and Kaller23). Recently, Diamond (Reference Diamond5) concluded from review of the literature that Gf can be regarded as being completely synonymous to the higher-level executive abilities reasoning and problem-solving.

The Kaufman Adolescent and Adult Intelligence Test (KAIT) is specifically designed to measure Gc and Gf (Reference Kaufman and Kaufman24). Apart from the Gf–Gc theory (Reference Horn and Cattell1), Luria’s neuropsychological theory of intelligence (Reference Luria25) as well as Piaget’s developmental concept of the formal-operational stage (Reference Piaget26), gave theoretical direction to the construction of the KAIT (Reference Kaufman, Lichtenberger and Kaufman2). Three widely used executive tasks from the Cambridge Neuropsychological Test Automated Battery (CANTAB) will be used to assess EF. The tasks include planning capacity and novel problem solving, working memory, reasoning, mental flexibility, and impulse control (Reference Robbins, James and Owen27). Although this is not an exhaustive sample of EF, a wide range of studied EF constructs is included, therefore, the CANTAB tasks representative measures of EF.

Method

Participants

Included were 188 participants (mean age 39.5±15.5, 51.6% male, n=98). This group consisted of 50 healthy individuals and 138 in- and outpatients of a neuropsychiatric department of a Dutch psychiatric hospital. See Table 1 for demographic variables.

Table 1 Demographics of the sample population

In accordance with the Diagnostic and Statistical Manual for Mental Disorders-Fourth Edition criteria, patients were diagnosed with major affective (including bipolar) disorders (44%), anxiety disorders (17%), impulsivity related psychopathology (9%), psychotic disorders (4%), dementia and other cognitive disorders (4%), developmental disorders (15%) and no formal psychiatric diagnosis (7%), respectively. Comorbidity with personality disorders was diagnosed in 37% of the patients.

For data analysis, patient identities were concealed. Informed consent was obtained from all healthy volunteers. Participants did not receive any compensation for participation. In accordance with the guidelines of the institutional review board, patient records were drawn from a large electronic database, containing test results of patients admitted in the period from May 2007 to December 2012. The majority of in- and outpatients received medical treatment to relieve symptoms of mental illness.

Results

Descriptive statistics for the nine measures of EF and intelligence are presented in Table 2. Correlations between all measures are shown in Table 3. No group differences in correlations are found for the sum-scores of Gf, Gc, and EF between the psychiatric patients and healthy participants (z-scores all <1.26, p-values all >0.20). Some values of skewness and kurtosis are significant. However, multiple studies have shown that the maximum likelihood estimator is robust, under general conditions, against deviations from normality (Reference Anderson and Amemiya36–Reference Satorra and Bentler38). Although the IED distribution approaches bimodality, this task is nevertheless included because it is necessary to examine the full scope of EF.

Table 2 Descriptive statistics for the KAIT subtests and CANTAB indices (n=188)

CANTAB, Cambridge Neuropsychological Test Automated Battery; KAIT, Kaufman Adolescent and Adult Intelligence Test.

*p<0.05.

Table 3 Intercorrelations of the KAIT subtests and CANTAB indices

CANTAB, Cambridge Neuropsychological Test Automated Battery; IED, Intra-Extra Dimensional Set Shift; KAIT, Kaufman Adolescent and Adult Intelligence Test; SOC, Stocking of Cambridge; SWM, Spatial Working Memory.

*p<0.05; **p<0.01.

We estimated a three-factor model to test our main hypothesis that Gf, Gc, and EF are correlated. Fig. 1 presents the estimated factor model. All factor loadings were significant (p<0.05) and >0.4. The model fitted the data [χ²(24)=35.25, p=0.07, RMSEA=0.050]. SWM loaded highest on EF, followed by SOC and IED, respectively, meaning this indicator contributed most to EF and to the EF–Gf relation.

Fig. 1 Structural Equation Modelling examining the relation between Gf and EF. Ellipses represent latent variables, squares represent manifest variables. The curved arrows represent correlations between the latent variables. The straight arrows to the left represent factor loadings, all significant at the .05 level. The small arrows to the right represent residual variances. Residual variances of the latent variables are fixed at 1.00. Negative values are the result of the operationalisation of the manifest variables using error scores. AC, Auditory Comprehension; D, Definitions; DM, Double Meanings; EF, Executive Functioning; Gc, Crystallized Intelligence; Gf, Fluid Intelligence; IED, Intra-Extra Dimensional Set Shift; LS, Logical Steps; MC, Mystery Codes; RL, Rebus Learning; SOC, Stockings of Cambridge; SWM, Spatial Working Memory.

It is not possible to directly test the hypothesis that the correlation between EF and Gf is higher than the correlation between EF and Gc. Instead, we tested whether the correlation between EF and Gc is equal to the correlation between EF and Gf. If so, then the hypothesis was rejected. If not, then we looked at the estimated correlations to draw conclusions. The extra constraints on the model were evaluated with the χ² difference test. We used the unrestricted three-factor model, as presented in Fig. 1, as the baseline model. The model with equality constraints on the correlations was rejected [χ²(25)=47.08, p=0.005, RMSEA=0.069]. The χ² difference test [χ²(1)=11.83] indicated that the extra constraint resulted in a significant increase of χ².

Given the high correlation between Gf and EF, similar restrictions were applied to test whether they are interchangeable (r _Gf–EF=1.00, r _Gc–Gf=r _Gc–EF). Model fit was moderate [χ²(26)=39.60, p=0.04, RMSEA=0.053], indicating that the two are statistically indistinguishable. We further verified the distinctiveness of this strong EF–Gf relation by comparing them to Gc. Constraints were applied to examine equality between Gf and Gc (r _Gf–Gc=1.00, r _EF–Gc=r _EF–Gf) and between all three constructs (r _Gf=r _Gc=r _EF). Both restricted models did not fit the data: [χ²(26)=74.79, p=0.00, RMSEA=0.100] and [χ²(26)=47.11, p=0.01, RMSEA=0.066], respectively.

Discussion

The present study examined the relation between EF and Gf in a mixed neuropsychiatric and non-clinical sample using the KAIT as a measure of Gf and Gc, and a selection of CANTAB tasks as a representation of EF. Results showed a significant correlation between Gf and EF, which were statistically indistinguishable in the current model. Working memory was a profound indicator for EF, represented in a high loading of SWM, followed by SOC. Current results are consistent with previous findings of a strong relation between Gf and working memory (Reference Friedman, Miyake, Corley, Young, DeFries and Hewitt8,Reference Duncan, Schramm, Thompson and Dumontheil20–Reference Unsworth and Engle22).

Looking at Table 3, SWM shows higher correlations with the KAIT fluid subtests than the other CANTAB tasks do. Although the fluid subscale of the KAIT is assumed to measure a broad scope of cognitive requirements (associative learning, sequencing, planning, syllogistic reasoning, mathematics, hypothetic-deductive reasoning and flexibility), spatial working memory seems to be an essential requirement for an adequate execution of the tasks. Hence, the structure of the KAIT and CANTAB was the starting point of the developed model. An alternative model with the SWM as predictor of Gf was not tested, since it would not contribute to the understanding of either the KAIT or CANTAB. Still, results strengthen the assumption that working memory plays a key role in understanding Gf (Reference Salthouse and Pink17).

Previously, underlying performance of complex cognitive tasks has been referred to as ‘executive attention’ or ‘cognitive control’ (Reference McCabe, Roediger, McDaniel, Balota and Hambrick9,Reference Kane, Hambrick, Tuholski, Wilhelm, Payne and Engle39). Similarly, Duncan’s (Reference Duncan, Schramm, Thompson and Dumontheil20,Reference Duncan40) description of the multiple demand (MD) system theory (Reference Duncan, Schramm, Thompson and Dumontheil20,Reference Duncan40) supports the view that EF and Gf share common processes. Essentially, it states that, when performing any set of (complex) actions, a task model is constructed. In this model, task components compete for representation. Adding new components to the model (e.g. new instructions) leads to more competition, making each component less robust or even lost. The efficiency of constructing such a task model is closely related to Gf, especially when task complexity and novelty increase (Reference Duncan, Schramm, Thompson and Dumontheil20). Since the CANTAB tasks are multi-faceted and increase in complexity compared with singular EF tasks (e.g. go/no-go paradigm), they may require more Gf involvement or MD activity, which in turn may explain the strong EF–Gf relation.

Current results have some implications for neuropsychiatric disease and treatment. Clinicians tend to strive for purity of cognitive constructs, which is reflected in commonly used neuropsychological instruments. Leaving the assemblage of Gf and EF out of account, interaction effects between these cognitive abilities, which are essential in the understanding and explanation of pathological behaviour, will be lost. This is in part due to the fact that most EF tasks are developed based on the diverse nature of EF, therefore not focusing on underlying common/general abilities. Following Diamond’s (Reference Diamond5) and Duncan’s (Reference Duncan, Schramm, Thompson and Dumontheil20,Reference Duncan40) theoretical position, deficits on task performance do not depend only on separate cognitive task demands, but on their context, that is, how they are put together to set up goal-directed behaviour. Therefore, the assessment of neuropsychological functioning should focus on dissecting the general process and efficiency of rule acquisition and application, next to examining specific cognitive skills necessary for task execution.

Some remarks about task-selection and data collection must be made. First, although CANTAB tasks can be considered as a realistic representation of EF in daily life, complexity seems to play such a crucial part in Gf involvement that utilisation of less multifaceted EF tasks could have resulted in a different outcome. The amount of general cognitive processes versus specific EF demands required for the tasks will influence this overlap. Second, the inclusion of the IED can be debated given its tendency towards a bimodal distribution. However, mental flexibility is of such importance in defining EF, that exclusion would undermine the a priori formulated model. Third, data collection was based on convenience sampling. Combining subsamples in one group allows us to include both high functioning and impaired participants and to examine the entire scope of EF and intelligence in a heterogeneous sample. A larger data set may allow future multi-group comparisons, using different psychiatric diagnostic groups and healthy participants, and/or different levels of severity in executive dysfunctioning.

A final comment concerns the theoretical framework. The current study adopts a neuropsychological perspective on EF, and based the model on the Gf–Gc distinction rather than on the more extensive Cattell-Horn-Carroll theory of cognitive abilities (CHC-theory; 41). In the latter, purity of abilities is essential in the psychometric perspective on intelligence, whereas the former neuropsychological view tends to be more integrative in describing different interacting abilities. Indeed, according to Kaufman and Kaufman (Reference Kaufman and Kaufman24) the fragmentation of intelligence does not contribute to clinical relevance, and therefore, CHC theory was not utilised in the construction of the KAIT. For further reading about CHC theory and neuropsychological constructs, see (Reference Schneider and Mcgrew41,Reference Flanagan, Alfonso, Ortiz and Dynda42).

In sum, results of the present study strengthen earlier findings on overlap of Gf and EF (Reference Roca, Manes and Cetkovich4,Reference Friedman, Miyake, Corley, Young, DeFries and Hewitt8,Reference Duncan, Parr and Woolgar43). Following Duncan’s theory on the MD system (Reference Duncan, Schramm, Thompson and Dumontheil20,Reference Duncan40), cumulating complexity will lead to more involvement of Gf, and may explain the current strong EF–Gf relation. Existing neuropsychological instruments are developed from a multiple-system view and do not separate specific executive task demands and ‘higher level’ general cognitive control required to execute the task. Furthermore, static outcome measures generally used in neuropsychological assessment do not give insight in the efficiency of task execution. Therefore, Gf dysfunction in neuropsychiatric patients warrants further EF examination and vice versa, to optimally enable discrimination between specific versus general cognitive dysfunctioning. Such a detailed analysis of the process of task execution (using both general intelligence tests as well as neuropsychological instruments) can guide differential diagnosis and lead to a more refined neuropsychiatric treatment indication.