The Catell-Horn-Caroll (CHC) theory of cognitive abilities consists of a taxonomy of cognitive abilities and a set of theoretical explanations of how and why people differ in their various cognitive abilities. This model builds on previous theories of intelligence (e.g. Spearman’s ‘g’; Gf-gc theory; early factor analysis).

A useful classification system shapes how we view complex phenomena by illuminating consequential distinctions and obscuring trivial differences. A misspecified classification system orients us toward the irrelevant and distracts us from taking productive action. Classification systems need to be properly aligned with our purposes.

The Gf-Gc theory states that general intelligence can be split into two separate general intelligence factors, namely into fluid intelligence (i.e. Gf) and crystallized intelligence (i.e. Gc). This theory is able to describe the nature of both factors. Cattell believed that the differences in breadth and depth of knowledge are influenced are the joint function of two influences. Fluid intelligence, as low fluid intelligence limits the rate at which a person can acquire and retain new knowledge (1) and investment, the differences in time and effort spent on learning (2). According to Cattell, this explains the positive manifold (i.e. differences in fluid intelligence and investment). The positive manifold (i.e. ‘g’) results from the differential success of investment due to fluid intelligence.

After the Gf-Gc theory, it was expanded to include several broad ability factors (e.g. visual intelligence). Later, Carroll’s three-stratum model, which consisted of a reanalysis of factor-analytic studies of human cognitive abilities. This model was the first empirically-based taxonomy of human cognitive abilities. His three-tier model differentiated abilities as functions of breadth. The broadest level (i.e. stratum III) is a general intelligence factor. Next in breadth, there are eight broad abilities that represent basic constitutional and long-standing characteristics of individuals that can govern or influence a great variety of behaviours in a given domain. Stratum II consists of the abilities of fluid and crystallized intelligence as well as other broad factors (e.g. broad auditory perception). Stratum I consists of numerous narrow abilities subsumed by the stratum II abilities. Critique is that none of the datasets included the necessary breadth of variables to evaluate the general structure of his model.

The WJ-R was the first individually administered, nationally standardized, clinical cognitive and achievement battery to close the gap between psychometric theory and applied assessment practice. It was an implementation of the multifactor model of intelligence.

CHC theory is an umbrella term variations on a Gf-Gc theme. This recognition increased because of CHC research syntheses. It was believed that the speed domains of Gs and Gt might best be represented within the context of a hierarchically organized speed taxonomy with a g-speed factor at the top.

It appears as if cognitive abilities contribute to academic achievement in different proportions in different domains. These proportions change over the course of development. Intelligence tests should be more flexible as one battery of tests does not fit all.

The 16-domain CHC model is embedded in an ability domain dimension that includes cognitive knowledge systems (1), cognitive operations (2), cognitive efficiency and cognitive control (3), sensory functions (4) and motor functions (5). An hierachically oganized CHC structrual diagram must be avoided because it may not explain natural phenomena well, as it is very artificial.

In the CHC model, there are domain-free general capacities:

1. Fluid reasoning (Gf)
   This refers to the deliberate but flexible control of attention to solve novel problems that cannot be performed by relying exclusively on previously learned habits, schemas and scripts. It is most evident in abstract reasoning. It is typically employed in accordance with background knowledge and automatized responses. It consists of induction (1), deductive reasoning (2) and quantitative reasoning (i.e. reasoning with numbers and mathematical relations) (3).
2. Short-term memory (Gsm)
   This refers to the ability to encode, maintain and manipulate information in one’s immediate awareness. Gsm refers to individual differences in capacity of primary memory and the efficiency of attentional control mechanisms that manipulate information in primary memory. It consists of several aspects.
   
   1. Memory span
      This refers to the ability to encode information, maintain it in primary memory and immediately reproduce the information in the same sequence in which it was represented
   2. Working memory capacity
      This refers to the ability to direct the focus of attention to perform relatively simple manipulations, combinations and transformations of information within primary memory, while avoiding distracting stimuli and engaging in controlled searches for information in secondary memory.
3. Long-term storage and retrieval (Glr)
   This refers to the ability to store, consolidate and retrieve information over periods of time. It is different from other acquired knowledge factors because long-term storage refers to the processes of memory. It consists of several aspects.
   
   1. Associative memory
      This refers to the ability to remember previously unrelated information as having been paired (e.g. chair, woman)
   2. Meaningful memory
      This refers to the ability to remember narratives and other forms of semantically related information (e.g. remembering the narrative of a story).
   3. Free-recall memory
      This refers to the ability to recall lists in any order.
   4. Ideational fluency
      This refers to the ability to rapidly produce a series of ideas, words or phrases related to a specific condition or object.
   5. Associational fluency
      This refers to the ability to rapidly produce a series of original or useful ideas related to a particular concept.
   6. Expressional fluency
      This refers to the ability to rapidly think of different ways of expression an idea.
   7. Sensitivity to problems (i.e. alternative solutions fluency)
      This refers to the ability to rapidly think of a number of alternative solutions to a particular practical problem.
   8. Originality (i.e. creativity)
      This refers to the ability to rapidly produce original, clever and insightful responses to a given topic, situation or task.
   1. Naming facility
      This refers to the ability to rapidly call objects by their names.
   10. Word fluency
       This refers to the ability to rapidly produce words that share a non-semantic feature.
   11. Figural fluency
       This refers to the ability to rapidly draw or sketch as many things as possible when presented with a non-meaningful visual stimulus.
   50. Figural flexibility
       This refers to the ability to rapidly draw different solutions to figural problems.
4. Processing speed (Gs)
   This refers to the ability to perform simple, repetitive cognitive tasks quickly and fluently. It is not an important predictor of skill learning but is an important predictor of skilled performance once people know how to do a task.
   
   1. Perceptual speed
      This refers to the speed at which visual stimuli can be compared for similarity or difference.
   2. Rate of test-taking
      This refers to the speed and fluency with which simple cognitive tests are completed.
   3. Number facility
      This refers to the speed at which basic arithmetic operations are performed accurately.
   4. Reading speed
      This refers to the rate of reading text with full comprehension.
   5. Writing speed
      This refers to the rate at which words or sentences can be generated or copied.
5. Reaction and decision speed (Gt)
   This refers to the speed of making very simple decisions or judgements when items are presented one at a time. Faster reaction times are associated with complex reasoning and greater consistency of reaction time (i.e. less variability).
   
   1. Simple reaction time
      This refers to the reaction time to the onset of a single stimulus.
   2. Choice reaction time
      This refers to the reaction time when a very simple choice must be made.
   3. Semantic processing speed
      This refers to the reaction time when a decision requires very simple encoding and mental manipulation of the stimulus content.
   4. Mental comparison speed
      This refers to the reaction time where stimuli must be compared for a particular characteristic or attribute.
   5. Inspection time
      This refers to the speed at which differences in stimuli can be perceived.
6. Psychomotor speed (Gps)
   This refers to the speed and fluidity with which physical body movements can be made.
   
   1. Speed of limb movement
      This refers to the speed of arm and leg movement.
   2. Writing speed
      This refers to the speed at which written words can be copied.
   3. Speed of articulation
      This refers to the ability to rapidly perform successive articulations.
   4. Movement time
      This refers to the time taken to physically move a body part to make the required response.

Long-term and short-term memory are interdependent. There needs to be a distinction between the ability to recall information in long-term and the fluency with which this information is retrieved. Primary memory refers to information that is in the current focus of attention. Secondary memory refers to memory that is not immediately accessible to consciousness. Memories that are unrelated to other memories are more difficult to recall. High retrieval fluency facilitates creativity.

There are several acquired-knowledge domains:

1. Comprehension knowledge (Gc)
   This refers to the depth and breadth of knowledge and skills that are valued by one’s culture. It cannot be measured independent of culture. Easy items should reveal important gaps in knowledge if they are answered incorrectly. Difficult items should reflect uncommon wisdom or it should be associated with deep knowledge of important aspects of one’s local culture.
   1. General verbal information
      This refers to the breadth and depth of knowledge that one’s culture deems essential, practical or worthwhile for everyone to know.
   2. Language development
      This refers to a general understanding of spoken language at the level of words, idioms and sentences.
   3. Lexical knowledge
      This refers to knowledge of the definitions of words and the concepts that underlie them.
   4. Listening ability
      This refers to the ability to understand speech.
   5. Communication ability
      This refers to the ability to use speech to communicate one’s thoughts clearly.
   6. Grammatical sensitivity
      This refers to the awareness of the formal rules of grammar and morphology of words in speech.
2. Domain-specific knowledge (Gkn)
   This refers to the depth, breadth and mastery of specialized knowledge. This is typically acquired via one’s hobby, passion or career. Domain-specific knowledge is influenced by non-ability variables (e.g. situational factors; individual interest). Expertise-wide span memory refers to the ability to accessing large amounts of specialized knowledge in long-term memory and hold it in immediate awareness.
   
   1. Foreign-language proficiency
      This refers to a general understanding of spoken language at the level of words, idioms and sentences for a foreign language. There is a different foreign-language proficiency for every language.
   2. Knowledge of signing
      This refers to the knowledge of finger spelling and signing (i.e. sign language).
   3. Skill in lip reading
      This refers to competence in the ability to understand communication from others by lip reading.
   4. Geography achievement
      This refers to having a range of geography knowledge.
   5. General science information
      This refers to having a range of scientific knowledge.
   6. Knowledge of culture
      This refers to having a range of knowledge about the humanities.
   7. Mechanical knowledge
      This refers to having a range of knowledge about the function, terminology and operation of tools, machines and equipment.
   8. Knowledge of behavioural content
      This refers to knowledge or sensitivity to non-verbal human communication.
3. Reading and writing (Grw)
   This refers to the depth and breadth of knowledge and skills related to written language.
   
   1. Reading decoding
      This refers to the ability to identify words from text.
   2. Reading comprehension
      This refers to the ability to understand written discourse.
   3. Reading speed
      This refers to the rate at which a person can read connected discourse with full comprehension.
   4. Spelling ability
      This refers to the ability to spell words.
   5. English usage
      This refers to knowledge of the mechanisms of writing (e.g. capitalization).
   6. Writing ability
      This refers to the ability to use text to communicate ideas clearly.
   7. Writing speed
      This refers to the ability to copy and generate text quickly.
4. Quantitative knowledge (Gq)
   This refers to the depth and breadth of knowledge related to mathematics.
   
   1. Mathematical knowledge
      This refers to a range of general knowledge about mathematics but not the performance of mathematical operations or solving math problems.
   2. Mathematical achievement
      This refers to measured mathematics achievement.

Sensory- and motor-linked abilities are linked to well-defined regions and functions of the cerebral cortex. Sensation refers to the detection of a stimulus. Perception refers to the complex processing of sensory information to extract relevant information from it. There are different types of sensory- and motor linked abilities.

1. Visual processing (Gv)
   This refers to the ability to make use of simulated mental imagery to solve problems. The results of low-level computations are used by higher-order processors to infer more complex aspects of the visual image. The tests measuring visual processing are designed to measure individual differences in these higher-order processes.
   1. Visualization
      This refers to the ability to perceive complex patterns and mentally simulate how they might look when transformed.
   2. Speeded relations
      This refers to the ability to solve problems quickly by using mental rotation of simple images.
   3. Closure speed
      This refers to the ability to quickly identify a familiar meaningful visual object from incomplete visual stimuli without knowing in advance what the object is (i.e. Gestalt perception).
   4. Flexibility of closure
      This refers to the ability to identify a visual figure or pattern embedded in a complex distracting or disguised visual pattern of array, when one knows in advance what the pattern is.
   5. Visual memory
      This refers to the ability to remember complex images over short periods of time.
   6. Spatial scanning
      This refers to the ability to visualize a path out of a maze or a field with many obstacles.
   7. Serial perceptual integration
      This refers to the ability to recognize an object after only parts of it are shown in rapid succession.
   8. Length estimation
      This refers to the ability to visually estimate the length of objects.
   1. Perceptual illusions
      This refers to the ability to not be fooled by visual illusions.
   10. Perceptual alternations
       This refers to the consistency in the rate of alternating between different visual perceptions.
   11. Imagery
       This refers to the ability to mentally produce very vivid images.
2. Auditory processing (Ga)
   This refers to the ability to detect and process meaningful non-verbal information in sound. Auditory processing depends on sensory input but it is not sensory input itself. It is also not the same as oral language comprehension.
   
   1. Phonetic coding
      This refers to the ability to hear phonemes distinctly. Poor phonetic coding is a major risk factor for reading disorder and leads people to have difficulties sounding out unfamiliar words.
   2. Speech sound discrimination
      This refers to the ability to detect and discriminate differences in speech sounds (i.e. non-phonemic aspects) under conditions of little or no distraction or distortion.
   3. Resistance to auditory stimulus distortion
      This refers to the ability to hear words correctly even under conditions of distortion or loud background noise.
   4. Memory for sound patterns
      This refers to the ability to retain auditory events.
   5. Maintaining and judging rhythm
      This refers to the ability to recognize and maintain a musical beat.
   6. Musical discrimination and judgement
      This refers to the ability to discriminate and judge tonal patterns in music with respect to melodic, harmonic and expressive aspects (e.g. tempo).
   7. Absolute pitch
      This refers to the ability to perfectly identify the pitch of tones.
   8. Sound localization
      This refers to the ability to localize heard sounds in space.
3. Olfactory abilities (Go)
   This refers to the abilities to detect and process meaningful information in odours. It does not refer to the sensitivity of the olfactory system but to the cognition one does with whatever information the nose is able to send. It can serve as an early indicator of neurological decline.
   
   1. Olfactory memory
      This refers to the ability to recognize previously encountered distinctive odours.
4. Tactile abilities (Gh)
   This refers to the abilities to detect and process meaningful information in touch sensations. It does not refer to the sensitivity of touch but to the cognition one does with tactile sensations.
5. Kinaesthetic abilities (Gk)
   This refers to the abilities to detect and process meaningful information in proprioceptive sensations.
6. Psychomotor abilities (Gp)
   This refers to the abilities to perform physical body motor movements with precision, coordination or strength.
   
   1. Static strength
      This refers to the ability to exert muscular force to move a relatively heavy or immobile object.
   2. Multilimb coordination
      This refers to the ability to make quick specific or discrete motor movements with the arms or legs.
   3. Finger dexterity
      This refers to the ability to make precisely coordinated movements of the fingers.
   4. Manual dexterity
      This refers to the ability to make precisely coordinated movements of a hand or a hand and the attached arm.
   5. Arm-hand steadiness
      This refers to the ability to precisely and skilfully coordinate arm-hand positioning in space.
   6. Control precision
      This refers to the ability to exert precise control over muscle movements, typically in response to environmental feedback.
   7. Aiming
      This refers to the ability to precisely and fluently execute a sequence of eye-hand coordination movements for positioning purposes.
   8. Gross body equilibrium
      This refers to the ability to maintain the body in an upright position in space or regain balance after balance has been disturbed.