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{{short description|Framework for scoring how complex a behavior is}}
The '''model of hierarchical complexity''' ('''MHC''') is a framework for scoring how complex a behavior is, such as [[Philosophy:Verbal reasoning|verbal reasoning]] or other cognitive tasks.<ref>Robinson, 2013</ref> It quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized, in terms of information science.<ref name="Commons2007">Commons, 2007</ref> This model was developed by Michael Commons and Francis Richards in the early 1980s.<ref name="Commonsetal1998"/>

==Overview==
The model of hierarchical complexity (MHC) is a [[Formal system|formal theory]] and a [[Mathematical psychology|mathematical psychology]] framework for scoring how complex a behavior is.<ref name="CommonsPekker2008">Commons & Pekker, 2008; Commons et al., 2014</ref> Developed by Michael Lamport Commons and colleagues,<ref name="Commonsetal1998">Commons et al., 1998</ref> it quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized,<ref>Coombs, Dawes, & Tversky, 1970</ref> in terms of information science.<ref name="CommonsRichards">Commons & Richards, 1984a, Commons & Richards, 1984b</ref><ref>Lindsay & Norman, 1977</ref><ref>Commons & Rodriguez, 1990, Commons & Rodriguez, 1993</ref> Its forerunner was the general stage model.<ref name="CommonsRichards"/>

Behaviors that may be scored include those of individual humans or their social groupings (e.g., organizations, governments, societies), animals, or machines. It enables scoring the hierarchical complexity of task accomplishment in any domain.<ref>Giri, Commons, & Harrigan, 2014; but for a different view see: Mascolo, 2008</ref> It is based on the very simple notions that higher order task actions:<ref name="Commons2007"/>
#are defined in terms of the next lower ones (creating hierarchy);
#organize the next lower actions;
#organize lower actions in a non-arbitrary way (differentiating them from simple chains of behavior).

It is cross-culturally and cross-species valid. The reason it applies cross-culturally is that the scoring is based on the mathematical complexity of the hierarchical organization of information. Scoring does not depend upon the content of the information (e.g., what is done, said, written, or analyzed) but upon how the information is organized.

The MHC is a non-[[Philosophy:Mentalism (psychology)|mentalistic]] model of developmental stages.<ref name="Commons2007"/> It specifies 16 orders of hierarchical complexity and their corresponding stages. It is different from previous proposals about developmental stage applied to humans;<ref>For example, Inhelder & Piaget, 1958</ref> instead of attributing behavioral changes across a person's age to the development of mental structures or [[Philosophy:Schema (psychology)|schema]], this model posits that task sequences of task behaviors form hierarchies that become increasingly complex. Because less complex tasks must be completed and practiced before more complex tasks can be acquired, this accounts for the developmental changes seen, for example, in individual persons' performance of complex tasks. (For example, a person cannot perform [[Arithmetic|arithmetic]] until the numeral representations of numbers are learned. A person cannot operationally multiply the sums of numbers until addition is learned. However, as much as natural intelligence helps human to understand some numbers, it does not play a complete role in multiplying large numbers without learning additions. 

The creators of the MHC claim that previous theories of stage have confounded the stimulus and response in assessing stage by simply scoring responses and ignoring the task or stimulus.<ref name="Commons2007"/> The MHC separates the task or stimulus from the performance. The participant's performance on a task of a given complexity represents the stage of developmental complexity.

Previous stage theories were unsatisfying to Commons and Richards because the theories did not show the existence of the stages more than describing sequential changes in human behavior. This led them to create a list of two concepts they felt a successful developmental theory should address. The two ideas they wanted to study were (1) the hierarchical complexity of the task to be solved and (2) the psychology, sociology, and anthropology of the task performance (and the development of the performance).<ref name="Commonsetal1998"/>

==Vertical complexity of tasks performed==
One major basis for this developmental theory is [[Philosophy:Task analysis|task analysis]]. The study of ideal tasks, including their instantiation in the real world, has been the basis of the branch of stimulus control called [[Physics:Psychophysics|psychophysics]]. Tasks are defined as sequences of contingencies, each presenting stimuli and each requiring a behavior or a sequence of behaviors that must occur in some non-arbitrary fashion. The complexity of behaviors necessary to complete a task can be specified using the horizontal complexity and vertical complexity definitions described below. Behavior is examined with respect to the analytically-known complexity of the task.

Tasks are quantal in nature. They are either completed correctly or not completed at all. There is no intermediate state (''tertium non datur''). For this reason, the model characterizes all stages as P-hard and functionally distinct. The orders of hierarchical complexity are [[Physics:Quantum|quantized]] like the [[Physics:Electron|electron]] atomic orbitals around the [[Physics:Atomic nucleus|nucleus]]: each task difficulty has an order of hierarchical complexity required to complete it correctly, analogous to the atomic [[Physics:Slater determinant|Slater determinant]]. Since tasks of a given quantified order of hierarchical complexity require actions of a given order of hierarchical complexity to perform them, the stage of the participant's task performance is equivalent to the order of complexity of the successfully completed task. The quantal feature of tasks is thus particularly instrumental in stage assessment because the scores obtained for stages are likewise discrete.

Every task contains a multitude of subtasks.<ref>Overton, 1990</ref> When the subtasks are carried out by the participant in a required order, the task in question is successfully completed. Therefore, the model asserts that all tasks fit in some configured sequence of tasks, making it possible to precisely determine the hierarchical order of task complexity. Tasks vary in complexity in two ways: either as ''horizontal'' (involving classical information); or as ''vertical'' (involving hierarchical information).<ref name="Commons2007"/>

===Horizontal complexity===
Classical information describes the number of "yes–no" questions it takes to do a task. For example, if one asked a person across the room whether a penny came up heads when they flipped it, their saying "heads" would transmit 1 bit of "horizontal" information. If there were 2 pennies, one would have to ask at least two questions, one about each penny. Hence, each additional 1-bit question would add another bit. Let us say they had a four-faced top with the faces numbered 1, 2, 3, and 4. Instead of spinning it, they tossed it against a backboard as one does with dice in a game of craps. Again, there would be 2 bits. One could ask them whether the face had an even number. If it did, one would then ask if it were a 2. Horizontal complexity, then, is the sum of bits required by just such tasks as these.

===Vertical complexity===
Hierarchical complexity refers to the number of [[Recursion|recursion]]s that the coordinating actions must perform on a set of primary elements. Actions at a higher order of hierarchical complexity: (a) are defined in terms of actions at the next lower order of hierarchical complexity; (b) organize and transform the lower-order actions (see Figure 2); (c) produce organizations of lower-order actions that are qualitatively new and not arbitrary, and cannot be accomplished by those lower-order actions alone. Once these conditions have been met, we say the higher-order action coordinates the actions of the next lower order.

To illustrate how lower actions get organized into more hierarchically complex actions, let us turn to a simple example. Completing the entire operation 3 × (4 + 1) constitutes a task requiring the [[Distributive property|distributive]] act. That act non-arbitrarily orders adding and multiplying to coordinate them. The distributive act is therefore one order more hierarchically complex than the acts of adding and multiplying alone; it indicates the singular proper sequence of the simpler actions. Although simply adding results in the same answer, people who can do both display a greater freedom of mental functioning. Additional layers of abstraction can be applied. Thus, the order of complexity of the task is determined through analyzing the demands of each task by breaking it down into its constituent parts.

The hierarchical complexity of a task refers to the number of [[Abstract algebra|concatenation]] operations it contains, that is, the number of recursions that the coordinating actions must perform. An order-three task has three concatenation operations. A task of order three operates on one or more tasks of vertical order two and a task of order two operates on one or more tasks of vertical order one (the simplest tasks).

==Stages of development==
[[Philosophy:Stage theory|Stage theories]] describe [[Biology:Human evolution|human]] organismic and/or [[Biology:Technological evolution|technological]] evolution as systems that move through a pattern of distinct stages over time. Here development is described formally in terms of the model of hierarchical complexity (MHC).

===Formal definition of stage===
Since actions are defined inductively, so is the function ''h'', known as the order of the hierarchical complexity. To each action ''A'', we wish to associate a notion of that action's hierarchical complexity, ''h(A)''. Given a collection of actions '''A''' and a participant ''S'' performing '''A''', the ''stage of performance'' of ''S'' on '''A''' is the highest order of the actions in '''A''' completed successfully at least once, i.e., it is: stage (''S'', '''A''') = max{''h(A)'' | ''A'' ∈ '''A''' and ''A'' completed successfully by ''S''}. Thus, the notion of stage is [[Classification of discontinuities|discontinuous]], having the same transitional gaps as the orders of hierarchical complexity. This is in accordance with previous definitions.<ref name="Commonsetal1998"/><ref>Commons & Miller, 2001</ref><ref name="CommonsPekker2008"/>

Because MHC stages are conceptualized in terms of the hierarchical complexity of tasks rather than in terms of mental representations (as in Piaget's stages), the highest stage represents successful performances on the most hierarchically complex tasks rather than intellectual maturity.

===Stages of hierarchical complexity===
The following table gives descriptions of each stage in the MHC.

{| class="wikitable"
|+Stages described in the model of hierarchical complexity (adapted from Commons, Crone-Todd, & Chen, 2014)
|-
! Order or stage
! What they do
! How they do it
! End result
|-
| 0 – calculatory
| Exact [[Computation|computation]] only, no [[Generalization|generalization]]
| Human-made programs manipulate 0, 1, not 2 or 3.
| Minimal human result. Unorganized machines (in [[Biography:Alan Turing|Turing]]'s sense) act in a way analogous to this stage.
|-
| 1 – automatic
| Engage in a single "hard-wired" action at a time, no respondent conditioning
| Respond, as a simple mechanism, to a single environmental stimulus
| Single celled organisms respond to a single stimulus in a way analogous to this stage
|-
| 2 – sensory and motor
| Discriminate in a rote fashion, [[Biology:Stimulus (physiology)|stimuli]] generalization, move
| Move limbs, lips, toes, eyes, elbows, head; view objects or move
| [[Philosophy:Experimental analysis of behavior#Philosophical basis of behavioral research|Discriminative]] establishing and reinforcing [[Philosophy:Classical conditioning|conditioned]] stimuli
|-
| 3 – circular sensory-motor
| Form open-ended [[Class (set theory)|proper classes]]
| Reach, touch, grab, shake objects, circular babble
| Open ended proper classes, [[Social:Phoneme|phoneme]]s, archiphonemes
|-
| 4 – sensory-motor
| Form [[Philosophy:Concept|concept]]s
| Respond to stimuli in a class successfully and non-stochastically
| [[Social:Morpheme|Morpheme]]s, concepts
|-
| 5 – nominal
| Find relations among concepts
| Use names for objects and other utterances as successful commands
| Single words: ejaculatives & exclamations, verbs, nouns, number names, letter names
|-
| 6 – sentential
| Imitate and acquire sequences; follow short sequential acts
| Generalize match-dependent task actions; chain words
| Various forms of pronouns: subject (I), object (me), possessive adjective (my), possessive pronoun (mine), and reflexive (myself) for various persons (I, you, he, she, it, we, y'all, they)
|-
| 7 – preoperational
| Make simple [[Deductive reasoning|deduction]]s; follow lists of sequential acts; tell stories
| Count [[Philosophy:Phenomenon|event]] roughly events and objects; connect the dots; combine numbers and simple [[Proposition|proposition]]s
| Connectives: as, when, then, why, before; products of simple operations
|-
| 8 – primary
| Simple [[Logic|logic]]al deduction and empirical rules involving time sequence; simple arithmetic
| Adds, subtracts, multiplies, divides, counts, proves, does series of tasks on own
| Times, places, counts acts, actors, arithmetic outcome, sequence from calculation
|-
| 9 – concrete
| Carry out full [[Arithmetic|arithmetic]], form cliques, plan deals
| Does [[Long division|long division]], short division, follows complex [[Philosophy:Convention (norm)|social rules]], ignores simple social rules, takes and coordinates [[Philosophy:Perspective (cognitive)|perspective]] of other and self
| Interrelations, social events, what happened among others, reasonable deals, history, geography
|-
| 10 – abstract
| Discriminate [[Variable (mathematics)|variables]] such as [[Philosophy:Stereotype|stereotype]]s; logical quantification; (none, some, all)
| Form variables out of finite classes; make and quantify propositions
| Variable time, place, act, actor, state, type; quantifiers (all, none, some); [[Philosophy:Categorical proposition|categorical assertions]] (e.g., "We all die")
|-
| 11 – formal
| Argue using empirical or logical [[Philosophy:Evidence|evidence]]; logic is linear, 1-dimensional
| Solve problems with one unknown using [[Algebra|algebra]], [[Logic|logic]] and [[Philosophy:Empiricism|empiricism]]
| Relationships (for example: [[Causality|causality]]) are formed out of variables; words: linear, logical, one-dimensional, if then, thus, therefore, because; correct scientific solutions
|-
| 12 – systematic
| Construct multivariate [[Philosophy:System|system]]s and [[Matrix (mathematics)|matrices]]
| Coordinate more than one variable as input; consider relationships in contexts.
| [[Philosophy:Phenomenon|Events]] and concepts situated in a multivariate context; systems are formed out of relations; systems: legal, societal, corporate, economic, [[Earth:Nation|nation]]al
|-
| 13 – metasystematic
| Construct multi-systems and metasystems out of disparate systems
| Create metasystems out of systems; compare systems and perspectives; name properties of systems: e.g. homomorphic, isomorphic, [[Philosophy:Completeness (logic)|complete]], consistent (such as tested by consistency proofs), [[Philosophy:Commensurability (philosophy of science)|commensurable]]
| Metasystems and supersystems are formed out of systems of relationships, e.g. [[Finance:Contract|contract]]s and promises
|-
| 14 – paradigmatic
| Fit metasystems together to form new [[Philosophy:Paradigm|paradigm]]s; show "incomplete" or "inconsistent" aspects of metasystems
| Synthesize metasystems
| Paradigms are formed out of multiple metasystems
|-
| 15 – cross-paradigmatic
| Fit paradigms together to form new fields
| Form new fields by crossing paradigms, e.g. [[Biology:Evolutionary biology|evolutionary biology]] + [[Biology:Developmental biology|developmental biology]] = [[Biology:Evolutionary developmental biology|evolutionary developmental biology]]
| New fields are formed out of multiple paradigms
|-
| 16 – meta-cross-paradigmatic (performative-recursive)
| Reflect on various properties of cross-paradigmatic operations
| Explicate the dynamics of, and limitations of, cross-paradigmatic thinking
| The dynamics and limitations of cross-paradigmatic thinking are explained as they are recursively enacted
|}

==Relationship with Piaget's theory==
The MHC builds on [[Piaget's theory of cognitive development|Piagetian theory]] but differs from it in many ways; notably the MHC has additional higher stages. In both theories, one finds:<ref name="Commons2007" />
<ol><li>Higher-order actions defined in terms of lower-order actions. This forces the hierarchical nature of the relations and makes the higher-order tasks include the lower ones and requires that lower-order actions are hierarchically contained within the relative definitions of the higher-order tasks.</li>
<li>Higher-order of complexity actions organize those lower-order actions. This makes them more powerful. Lower-order actions are organized by the actions with a higher order of complexity, i.e., the more complex tasks.</li></ol>

What Commons et al. (1998) have added includes:
<ol start="3"><li>Higher-order-of-complexity actions organize those lower-order actions in a non-arbitrary way.</li></ol>

This makes it possible for the model's application to meet real world requirements, including the empirical and analytic. Arbitrary organization of lower order of complexity actions, possible in the Piagetian theory, despite the hierarchical definition structure, leaves the functional correlates of the interrelationships of tasks of differential complexity formulations ill-defined.

Moreover, the model is consistent with the [[Philosophy:Neo-Piagetian theories of cognitive development|neo-Piagetian theories of cognitive development]]. According to these theories, progression to higher stages or levels of cognitive development is caused by increases in processing efficiency and [[Working memory|working memory]] capacity. That is, higher-order stages place increasingly higher demands on these functions of information processing, so that their order of appearance reflects the information processing possibilities at successive ages.<ref>Demetriou, 1998</ref>

The following dimensions are inherent in the application:<ref name="Commons2007"/>
# Task and performance are separated.
# All tasks have an order of hierarchical complexity.
# There is only one sequence of orders of hierarchical complexity.
# Hence, there is structure of the whole for [[Ideal tasks|ideal tasks]] and actions.
# There are transitional gaps between the orders of hierarchical complexity.
# Stage is defined as the most hierarchically complex task solved.
# There are discrete gaps in [[Rasch model|Rasch scaled]] stage of performance.
# Performance stage is different task area to task area.
# There is no structure of the whole—horizontal décalage—for performance. It is not inconsistency in thinking within a developmental stage. Décalage is the normal modal state of affairs.

==Orders and corresponding stages==
The MHC specifies 16 orders of hierarchical complexity and their corresponding stages, positing that each of Piaget's substages, in fact, are robustly hard stages.<ref name="CommonsCroneToddChen2014">Commons, Crone-Todd, & Chen, 2014</ref> The MHC adds five postformal stages to Piaget's developmental trajectory: systematic stage 12, metasystematic stage 13, paradigmatic stage 14, cross-paradigmatic stage 15, and meta-cross-paradigmatic stage 16. It may be the Piaget's ''consolidate'' formal stage is the same as the ''systematic'' stage. The sequence is as follows: (0) calculatory, (1) automatic, (2) sensory & motor, (3) circular sensory-motor, (4) sensory-motor, (5) nominal, (6) sentential, (7) preoperational, (8) primary, (9) concrete, (10) abstract, (11) formal, and the five postformal: (12) systematic, (13) metasystematic, (14) paradigmatic, (15) cross-paradigmatic, and (16) meta-cross-paradigmatic. The first four stages (0–3) correspond to Piaget's sensorimotor stage at which infants and very young children perform. Adolescents and adults can perform at any of the subsequent stages. MHC stages 4 through 5 correspond to Piaget's pre-operational stage; 6 through 8 correspond to his concrete operational stage; and 9 through 11 correspond to his formal operational stage.

More complex behaviors characterize multiple system models.<ref>Kallio, 1995; Kallio & Helkama, 1991</ref> The four highest stages in the MHC are not represented in Piaget's model. The higher stages of the MHC have extensively influenced the field of positive adult development. Some adults are said to develop alternatives to, and perspectives on, formal operations; they use formal operations within a "higher" system of operations. Some theorists call the more complex orders of cognitive tasks "[[Philosophy:Postformal thought|postformal thought]]", but other theorists argue that these higher orders cannot exactly be labelled as postformal thought.<ref>Kallio, 2011</ref>

Jordan (2018) argued that unidimensional models such as the MHC, which measure level of complexity of some behavior, refer to only one of many aspects of adult development, and that other variables are needed (in addition to unidimensional measures of complexity) for a fuller description of adult development.

==Empirical research using the model==
The MHC has a broad range of applicability.<ref name="Commons2007"/> Its mathematical foundation permits it to be used by anyone examining task performance that is organized into stages. It is designed to assess development based on the order of complexity which the actor utilizes to organize information. The model thus allows for a standard quantitative analysis of developmental complexity in any cultural setting. Other advantages of this model include its avoidance of [[Philosophy:Mentalism (psychology)|mentalistic]] explanations, as well as its use of quantitative principles which are universally applicable in any context.<ref name="Commons2007"/>

The following practitioners can use the MHC to quantitatively assess developmental stages:<ref name="Commons2007"/>
* Cross-cultural developmentalists
* [[Biology:Animal cognition|Animal developmentalist]]s
* Evolutionary psychologists
* [[Social:Industrial and organizational psychology|Organizational psychologist]]s
* Developmental [[Social:Political psychology|political psychologist]]s
* [[Philosophy:Learning theory (education)|Learning theorist]]s
* [[Perception]] researchers
* [[History:History of science|Historians of science]]
* Educators
* [[Medicine:Therapist|Therapist]]s
* Anthropologists

===List of examples===
In one representative study, Commons, Goodheart, and Dawson (1997) found, using [[Rasch model|Rasch analysis]] (Rasch, 1980), that hierarchical complexity of a given task predicts stage of a performance, the correlation being r = 0.92. Correlations of similar magnitude have been found in a number of the studies. The following are examples of tasks studied using the model of hierarchical complexity or [[Biography:Kurt W. Fischer|Kurt W. Fischer]]'s similar skill theory:<ref name="Commons2007"/>
{{Div col|colwidth=30em}}
* Algebra (Commons, Giri, & Harrigan, 2014)
* Animal stages (Commons & Miller, 2004)
* Atheism (Commons-Miller, 2005)
* Attachment and loss (Commons, 1991; Miller & Lee, 2000)
* Balance beam and pendulum (Commons, Goodheart, & Bresette, 1995; Commons, Giri, & Harrigan, 2014)
* Contingencies of reinforcement (Commons & Giri, 2016)
* Counselor stages (Lovell, 2002)
* Empathy of hominids (Commons & Wolfsont, 2002)
* Epistemology (Kitchener & Fischer, 1990; Kitchener & King, 1990)
* Evaluative reasoning (Dawson, 2000)
* Four story problem (Commons, Richards & Kuhn, 1982; Kallio & Helkama, 1991)
* Good education (Dawson-Tunik, 2004)
* Good interpersonal relations (Armon, 1984a; Armon, 1984b; Armon, 1989)
* Good work (Armon, 1993)
* Honesty and kindness (Lamborn, Fischer & Pipp, 1994)
* Informed consent (Commons & Rodriguez, 1990; Commons & Rodriguez, 1993; Commons, Goodheart, Rodriguez, & Gutheil, 2006)
* Language stages (Commons et al., 2007)
* Leadership before and after crises (Oliver, 2004)
* Loevinger's sentence completion task (Cook-Greuter, 1990)
* Moral judgment (Armon & Dawson, 1997; Dawson, 2000)
* Music (Beethoven) (Funk, 1989)
* Physics tasks (Inhelder & Piaget, 1958)
* Political development (Sonnert & Commons, 1994)
* Report patient's prior crimes (Commons, Lee, Gutheil, et al., 1995)
* Social perspective-taking (Commons & Rodriguez, 1990; Commons & Rodriguez, 1993)
* Spirituality (Miller & Cook-Greuter, 1994)
* Tool making of hominids (Commons & Miller 2002)
* Views of the good life (Armon, 1984b; Danaher, 1993; Dawson, 2000; Lam, 1995)
* Workplace culture (Commons, Krause, Fayer, & Meaney, 1993)
* Workplace organization (Bowman, 1996)
{{Div col end}}

As of 2014, people and institutes from all the major continents of the world, except Africa, have used the model of hierarchical complexity.<ref name="CommonsChen2014">Commons & Chen, 2014</ref> Because the model is very simple and is based on analysis of tasks and not just performances, it is dynamic.<ref name="CommonsChen2014"/> With the help of the model, it is possible to quantify the occurrence and progression of transition processes in task performances at any order of hierarchical complexity.<ref>Ross, 2014</ref>

==Criticisms==
The descriptions of stages 13–15 have been described as insufficiently precise.<ref>Young, 2011</ref><ref>Ross et al., 2014</ref>

==See also==
{{Div col}}
* {{annotated link|Philosophy:Behavior analysis of child development}}
* {{annotated link|Bloom's taxonomy}}
* {{section link|Coherence therapy|Hierarchical organization of constructs}}
* {{annotated link|Philosophy:Constructive developmental framework}}
* {{annotated link|Biology:Developmental systems theory}}
* {{annotated link|DIKW pyramid}}
* {{annotated link|Educational assessment}}
* {{annotated link|Social:Elementary cognitive task}}
* {{annotated link|Philosophy:Higher-order thinking}}
* {{annotated link|Social:Instructional scaffolding}}
* {{annotated link|Integrative level}}
* {{annotated link|Philosophy:Lawrence Kohlberg's stages of moral development}}
* {{annotated link|Biology:Metasystem transition}}
* {{annotated link|Rubric (academic)}}
* {{annotated link|Second-order cybernetics}}
* {{annotated link|Structure of observed learning outcome}}
{{Div col end}}

==References==
{{reflist|colwidth=20em}}

==Literature==
{{refbegin|30em}}
* {{Wikicite |id=Armon1984a |reference=Armon, C. (1984a). Ideals of the good life and moral judgment: Ethical reasoning across the life span. In M.L. Commons, F.A. Richards, & C. Armon (Eds.), ''Beyond formal operations: Vol. 1. Late adolescent and adult cognitive development'' (pp.&nbsp;357–380). New York: Praeger.}}
* {{Wikicite |id=Armon1984b |reference=Armon, C. (1984b). Ideals of the good life and moral judgment: Evaluative reasoning in children and adults. ''Moral Education Forum'', 9(2).}}
* {{Wikicite |id=Armon1989 |reference=Armon, C. (1989). Individuality and autonomy in adult ethical reasoning. In M.L. Commons, J.D. Sinnott, F.A. Richards, & C. Armon (Eds.), ''Adult development, Vol. 1. Comparisons and applications of adolescent and adult developmental models'', (pp.&nbsp;179–196). New York: Praeger.}}
* {{Wikicite |id=Armon1993 |reference=Armon, C. (1993). The nature of good work: A longitudinal study. In J. Demick & P.M. Miller (Eds.), ''Development in the workplace'' (pp.&nbsp;21–38). Hillsdale, NJ: Erlbaum.}}
* {{Wikicite |id=ArmonDawson1997 |reference=Armon, C. & Dawson, T.L. (1997). Developmental trajectories in moral reasoning across the life-span. ''Journal of Moral Education'', 26, 433–453.}}
* Biggs, J.B. & Collis, K. (1982). ''Evaluating the quality of learning: The SOLO taxonomy (structure of the observed learning outcome)''. New York: Academic Press.
* {{Wikicite |id=Bowman1996 |reference=Bowman, A.K. (1996). Examples of task and relationship 4b, 5a, 5b statements for task performance, atmosphere, and preferred atmosphere. In M.L. Commons, E.A. Goodheart, T.L. Dawson, P.M. Miller, & D.L. Danaher, (Eds.) ''The general stage scoring system (GSSS)''. Presented at the Society for Research in Adult Development, Amherst, MA.}}
* {{Wikicite |id=Commons1991 |reference=Commons, M.L. (1991). A comparison and synthesis of Kohlberg's cognitive-developmental and Gewirtz's learning-developmental attachment theories. In J.L. Gewirtz & W.M. Kurtines (Eds.), ''Intersections with attachment'' (pp.&nbsp;257–291). Hillsdale, NJ: Erlbaum.}}
* {{Wikicite |id=Commons2007 |reference=Commons, M.L. (2007). Introduction to the model of hierarchical complexity. ''Behavioral Development Bulletin'', 13(1), 1–6.}}
* {{Wikicite |id=CommonsChen2014 |reference=Commons, M.L., & Chen, S.J. (2014). Advances in the model of hierarchical complexity (MHC). ''Behavioral Development Bulletin'', 19(4), 37–50.}}
* {{Wikicite |id=CommonsCroneToddChen2014 |reference=Commons, M.L., Crone-Todd, D., & Chen, S.J. (2014). Using SAFMEDS and direct instruction to teach the model of hierarchical complexity. ''The Behavior Analyst Today'', 14(1-2), 31–45.}}
* {{Wikicite |id=Commonsetal2014 |reference=Commons, M.L., Gane-McCalla, R., Barker, C.D., & Li, E.Y. (2014). The model of hierarchical complexity as a measurement system. ''Behavioral Development Bulletin'', 19(3), 9–14.}}
* {{Wikicite |id=CommonsGiri2016 |reference=Commons, M.L., & Giri, S. (2016). Account of operant conditioning based on coordinating three procedural steps of respondent conditioning processes. ''Behavioral Development Bulletin'', 21(1), 14–32.}}
* {{Wikicite |id=CommonsGiriHarrigan2014 |reference=Commons, M.L., Giri, S., & Harrigan, W.J. (2014). The small effects of non-hierarchical complexity variables on performance. ''Behavioral Development Bulletin'', 19(4), 31–36.}}
* {{Wikicite |id=CommonsGoodheartBresette1995 |reference=Commons, M.L., Goodheart, E.A., & Bresette, L.M. with Bauer, N.F., Farrell, E.W., McCarthy, K.G., Danaher, D.L., Richards, F.A., Ellis, J.B., O'Brien, A.M., Rodriguez, J.A., and Schraeder, D. (1995). Formal, systematic, and metasystematic operations with a balance-beam task series: A reply to Kallio's claim of no distinct systematic stage. ''Adult Development'', 2 (3), 193–199.}}
* {{Wikicite |id=CommonsGoodheartDawson1997 |reference=Commons, M.L., Goodheart, E.A., & Dawson T.L. (1997). ''Psychophysics of stage: Task complexity and statistical models''. Paper presented at the International Objective Measurement Workshop at the Annual Conference of the American Educational Research Association, Chicago, IL.}}
* {{Wikicite |id=Commonsetal2007 |reference=Commons, M.L., Goodheart, E.A., Pekker, A., Dawson, T.L., Draney, K., & Adams, K.M. (2007). Using Rasch scaled stage scores to validate orders of hierarchical complexity of balance beam task sequences. In E.V. Smith, Jr. & R.M. Smith (Eds.). ''Rasch measurement: Advanced and specialized applications'' (pp.&nbsp;121–147). Maple Grove, MN: JAM Press.}}
* {{Wikicite |id=CommonsGoodheartRodriguezGutheil2006 |reference=Commons, M.L., Goodheart, E.A., Rodriguez, J.A., Gutheil, T.G. (2006). Informed Consent: Do you know it when you see it? ''Psychiatric Annals'', June, 430–435.}}
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{{refend}}

==External links==
{{Library resources box|by=no|onlinebooks=no|about=yes|wikititle=model of hierarchical complexity}}
* [http://www.behavioraldevelopmentbulletin.com Behavioral Development Bulletin]
* [http://adultdevelopment.org Society for Research in Adult Development]

{{DEFAULTSORT:Model of hierarchical complexity}}
[[Category:Cognition]]
[[Category:Complex systems theory]]

{{Sourceattribution|Model of hierarchical complexity}}