wobbles, humps and sudden jumps1 A theoretical reflection on the nature of psychological properties …

wobbles, humps and sudden jumps - theoretical reflection2 Dynamic view of psychological phenomena The principal focus is on the individual person For whom actions, thoughts, concepts, skills, … Are the product of a real-time construction process that requires organismic and contextual components that emerges out of the interplay between organism and context The principal focus is on the individual person For whom actions, thoughts, concepts, skills, … Are the product of a real-time construction process that requires organismic and contextual components that emerges out of the interplay between organism and context If this is our framework, … And we wish to measure psychological variables/properties … We are confronted with a rather serious difficulty... If this is our framework, … And we wish to measure psychological variables/properties … We are confronted with a rather serious difficulty...

wobbles, humps and sudden jumps - theoretical reflection3 Why? Measurement = Attribution of a specific property (variable) as a definite property of a person But, according to a dynamic/contextualist view There are no such properties of persons “there is no object concept in the child, it’s assembled each time the child is in a context that requires it…” Error handling requires Conditional Independence but in an individual process, the next step usually depends on the preceding one: conditional dependence The structure of variability across a group  structure of variability across an individual process (Molenaar) Measurement = Attribution of a specific property (variable) as a definite property of a person But, according to a dynamic/contextualist view There are no such properties of persons “there is no object concept in the child, it’s assembled each time the child is in a context that requires it…” Error handling requires Conditional Independence but in an individual process, the next step usually depends on the preceding one: conditional dependence The structure of variability across a group  structure of variability across an individual process (Molenaar) A dynamic, process-oriented, contextualist view requires a rethinking of psychometric axioms… What is the nature of a psychological property, how should it be measured and represented? A dynamic, process-oriented, contextualist view requires a rethinking of psychometric axioms… What is the nature of a psychological property, how should it be measured and represented?

wobbles, humps and sudden jumps - theoretical reflection4 The color of her socks… (1 of 2) What is the color of her socks? Yellow… The color cannot be observed directly (she won’t show you, she’s too prudish) But she will tell you the color by pointing at a spot on a color chart Possibility of Measurement Error!! Both the color of the socks she wears and the color spot she points at are determinate properties… Difference between the spot and the true color = measurement error Both the color of the socks she wears and the color spot she points at are determinate properties… Difference between the spot and the true color = measurement error

wobbles, humps and sudden jumps - theoretical reflection5 The color of her socks… (2 of 2) What is the color of the socks that she will wear tomorrow? The color has not yet been determined… anything goes? No, we can provide information about tomorrow’s color By specifying constraints on the degrees of freedom Based on the socks in her drawer, socks that are in the wash, the color she was wearing today, … The color of the socks she will be wearing tomorrow is an indeterminate property Which can be described by specifying constraints on degrees of freedom The color of the socks she will be wearing tomorrow is an indeterminate property Which can be described by specifying constraints on degrees of freedom

wobbles, humps and sudden jumps - theoretica lreflection6 Back to psychological properties… (1 of 2) The standard view Just like the color of the socks she is wearing, but refuses to show … Psychological properties are determinate properties (fixed or true value) But they are covert, latent, concealed, … And thus, must be measured indirectly, which implies measurement error (I.e variability in the measure) Example: true score theory Observed score = true score + error Example: “true category” theory Object Concept, ADHD The standard view Just like the color of the socks she is wearing, but refuses to show … Psychological properties are determinate properties (fixed or true value) But they are covert, latent, concealed, … And thus, must be measured indirectly, which implies measurement error (I.e variability in the measure) Example: true score theory Observed score = true score + error Example: “true category” theory Object Concept, ADHD

wobbles, humps and sudden jumps - theoretical reflection7 Back to psychological properties… (2 of 2) The contextualist view What we call psychological properties are properties that become determinate in a specific context, action,.. They fluctuate and vary.. However, we wish to make statements about such properties that go beyond an actual situation In that sense, psychological properties are indeterminate properties They are specified by describing constraints on the degrees of freedom The contextualist view What we call psychological properties are properties that become determinate in a specific context, action,.. They fluctuate and vary.. However, we wish to make statements about such properties that go beyond an actual situation In that sense, psychological properties are indeterminate properties They are specified by describing constraints on the degrees of freedom

wobbles, humps and sudden jumps - theoretical reflection8 Measurement error The standard view (1 of 2) We need a ruler... We are dealing with determinate, but “hidden” properties … We need a ruler... We are dealing with determinate, but “hidden” properties …

wobbles, humps and sudden jumps - theoretical reflection9 The standard view (2 of 2) The score is based on a probability… Which can, in principle, be sampled an infinite number of times … Each sample is, in principle, independent of any other one … The score is based on a probability… Which can, in principle, be sampled an infinite number of times … Each sample is, in principle, independent of any other one … The true value of the variable… Is a hidden but determinate property: The average of all the values that can be sampled from a probability distribution Which implies (in principle) the possibility of infinite sampling independent sampling The true value of the variable… Is a hidden but determinate property: The average of all the values that can be sampled from a probability distribution Which implies (in principle) the possibility of infinite sampling independent sampling

wobbles, humps and sudden jumps - theoretical reflection10 An alternative view (1 of 6) We need a ruler to specify an indeterminate property We learn about this property by measuring a number of determinate cases And then use this information to specify the indeterminate property as constraints on the degrees of freedom By specifying a characteristic range (instead of a true score) We need a ruler to specify an indeterminate property We learn about this property by measuring a number of determinate cases And then use this information to specify the indeterminate property as constraints on the degrees of freedom By specifying a characteristic range (instead of a true score)

wobbles, humps and sudden jumps - theoretical reflection11 An alternative view (2 of 6) characteristicness Range of characteristic scores Range of uncharacteristic scores The white trapezium line specifies the characteristicness (0 to 1) of the corresponding scores. It corresponds with a standard function from Fuzzy Logic, namely the degree-of-membership function. It specifies the degree-of-membership of all possible scores, to the set of characteristic scores. The function specifies an open set of scores. The open set corresponds with the notion of an indeterminate property (properties that have yet to be determined, but are governed by constraints) The membership (or characteristicness) function characterizes an individual person implies both person and context properties (the person’s characteristic contexts) is not a probability function The white trapezium line specifies the characteristicness (0 to 1) of the corresponding scores. It corresponds with a standard function from Fuzzy Logic, namely the degree-of-membership function. It specifies the degree-of-membership of all possible scores, to the set of characteristic scores. The function specifies an open set of scores. The open set corresponds with the notion of an indeterminate property (properties that have yet to be determined, but are governed by constraints) The membership (or characteristicness) function characterizes an individual person implies both person and context properties (the person’s characteristic contexts) is not a probability function

wobbles, humps and sudden jumps - theoretical reflection12 An alternative view (3 of 6) characteristicness Uncharacteristic score If it occurs, the context is prob- ably highly uncharacteristic … Or, the dynamic process that leads to the score is probably anomalous … Likelihood: very low Characteristic score If it occurs, the context and/or the dynamic process that leads to the score is probably highly characteristic. Likelihood: high “Not very” characteristic score If it occurs, the context and/or the dynamic process that leads to the score are probably “not very” characteristic. Likelihood: relatively high The members of the open set of scores are actual scores, i.e actual measurements or observations. The open set of scores has A characteristic number of members (measurements, observations) Which have a characteristic temporal order (note the difference with a probability distribution) The membership (or characteristicness) function need not be unimodal, but can also be bimodal or n-modal The property of modality can be used to describe different forms of developmental transitions The members of the open set of scores are actual scores, i.e actual measurements or observations. The open set of scores has A characteristic number of members (measurements, observations) Which have a characteristic temporal order (note the difference with a probability distribution) The membership (or characteristicness) function need not be unimodal, but can also be bimodal or n-modal The property of modality can be used to describe different forms of developmental transitions

wobbles, humps and sudden jumps - theoretical reflection13 An alternative view (4 of 6) characteristicness Ranges need not be unimodal … Multimodality: e.g. two sets of constraints and two corresponding ranges Ranges need not be unimodal … Multimodality: e.g. two sets of constraints and two corresponding ranges Examples Fischer: testing with and without support, optimal and functional level Goldin-Meadow and Alibali: different modes of thought under different forms of expression Van der Maas and Molenaar: simultaneous modes of conservation Examples Fischer: testing with and without support, optimal and functional level Goldin-Meadow and Alibali: different modes of thought under different forms of expression Van der Maas and Molenaar: simultaneous modes of conservation

wobbles, humps and sudden jumps - theoretical reflection14 An alternative view (5 of 6) A range is not a probability infinite sampling, conditional independence The dynamics of a variable determine its sampling characteristics Characteristic sampling order Repeated measurement of ToM in normal children: learning effect and increase in score In PDD-NOS children, repeated testing causes a significant drop in the scores Dynamic testing characteristic sampling frequency Language use <> self and identity discourse

wobbles, humps and sudden jumps - theoretical reflection15 If you sample from a range, it will have a characteristic order and frequency An alternative view (6 of 6) characteristicness Taking a test is an action … People learn from their actions (dynamic testing) Taking a test is an action … People learn from their actions (dynamic testing)

wobbles, humps and sudden jumps - theoretical reflection16 A toolbox of rulers The variable ruler Specifying both determinate and indeterminate properties e.g. a test, frequencies The characteristicness ruler Degree of characteristicness Applies to properties of the person as well as the environment The time line: short-, middle and long-term change The degree-of-membership ruler Diagnostic categories, linguistic categories, … The variable ruler Specifying both determinate and indeterminate properties e.g. a test, frequencies The characteristicness ruler Degree of characteristicness Applies to properties of the person as well as the environment The time line: short-, middle and long-term change The degree-of-membership ruler Diagnostic categories, linguistic categories, …