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Transitions over variables: assigning categories

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wobbles, humps and sudden jumps. 1. Transitions over ... wobbles, humps and sudden jumps - transitions over variables. 2. Assigning categories (1 of 2) ... – PowerPoint PPT presentation

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Title: Transitions over variables: assigning categories


1
Transitions over variables assigning categories
2
Assigning categories (1 of 2)
  • Indicator variable is often a frequency of
    occurrence or an intensity
  • How much of an indicator variable should there be
    in order for a category to be there?
  • How many prepositions must an infant use so that
    we can say that the preposition category is
    present?
  • How hyperactive must a child be in order to count
    as hyperactive?
  • How stable must the childs sociometric choices
    be in order to count as stable?
  • Examples
  • Does the child have prepositions, object
    concept, .. Or not
  • ADHD or not, PDD-Nos or not,
  • Is the childs sociometric rating stable or
    not..?
  • Standard Assumptions
  • Category is a determinate property
  • Mutually exclusive categories
  • Observer disagreement is error
  • Assignment often based on
  • Continuous indicator variables
  • A number of such indicators

3
Assigning categories (2 of 2)
4
Categories as a transition problem (1 of 3)
  • Method
  • Define stable rating as any rating that is based
    on stronger rating constraints than those of your
    null-hypothesis model
  • Define a null-hypothesis model. E.g.
  • No rating constraints
  • No stronger rating constraints than gender
    preference
  • Run null-hypothesis model many times
  • Determine probability that null model produces
    agreement between ratings that are as good as or
    better than observed agreements between ratings
  • The probability specifies a transition function
  • Example when are the social preferences
    stable?
  • actual preference determinate property
    preference in general indeterminate property
  • Preference in general can be expressed in terms
    of constraints on choices
  • If those constraints are obeyed, then the rating
    is stable
  • Ratings are stable if they cannot be produced by
    a rating where such constraints are absent

5
Categories as a transition problem (3 of 3)
  • Results
  • Transition curve depends on the properties of the
    null-model (i.e. a model with no constraints, or
    not enough constraints) and on the number/nature
    of ratings given by a child
  • The form of the transition curve makes it easy to
    divide the -of-agreement dimension in three
    categories
  • Stable raters (more constraints than null-model)
  • Variable raters (consistent variation)
  • Transition group ambiguous state, or both
  • The childs preference is either an actual choice
    (determinate property) or an indeterminate
    property (range) the child occupies a range on
    the stability dimension (how stable is the
    childs stability?)

6
Categories as a transition problem (3 of 3)
The stability of a child is also represented by a
range
7
Transition curves and fuzzy categories
  • Example prepositions
  • When is a preposition a preposition?
  • How many prepositions should the child produce
    before we can say that it has the preposition
    category?
  • In language development, categories, such as
    prepositions, are constructed
  • The construction process can be described by a
    transition curve
  • During the process, the child will go through a
    phase of ambiguity

8
A note on interobserver (dis)agreement
  • Disagreement in categorization of behaviors seen
    as error
  • We correct for chance agreement (e.g. Kappa)
  • The reasoning behind the chance correction is
    strange
  • Disagreement contains information If categories
    are ambiguous, disagreement among competent
    observers reflects the ambiguity of the observed
    category
  • Transform disagreement into a measure of
    ambiguity or a measure of the fuzziness of the
    categories

9
Recapitulation
10
Recapitulation (1 of 3)
  • I started from a dynamic and contextual view on
    developing behavior
  • And applied the distinction between determinate
    and indeterminate properties to measuring actual
    behavior versus making a statement about
    capacities, abilities generalizing over actual
    contexts
  • Measured properties are indeterminate
  • And can be represented as specific constraints on
    the degrees of freedom
  • Which amounts to specifying ranges instead of
    true scores or levels

11
Recapitulation (2 of 3)
  • I used this view to study developmental
    transitions and claimed such transitions are
    intimately linked to variability
  • I made a distinction between transitions over
    time and transitions over descriptive variables
    (categorization)
  • A distinction was made between continuous and
    discontinuous transitions
  • A common property is the occurrence of anomalies
  • I demonstrated techniques for describing and
    testing those anomalies

12
Recapitulation (3 of 3)
  • I showed how categorization can be viewed a s a
    form of transition over a descriptive category
  • And demonstrated a method to make a distinction
    between stable and unstable sociometric
    ratings
  • I argued that categorization is intimately linked
    to ambiguity and fuzziness
  • Ambiguity and fuzziness can be quantified in
    terms of transition functions
  • Disagreement among (trained and competent)
    observers may provide information about ambiguity

But basically I have argued that a dynamic and
contextual view on development requires a
rethinking of measurement and a renewed interest
in the study of phenomena that have suffered from
too much suspicion, namely intra-individual
variability, extremes, anomalies, ambiguity,
fuzziness and yellow socks.
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