Akaike information criterion

(noun)

a measure of the relative quality of a statistical model, for a given set of data, that deals with the trade-off between the complexity of the model and the goodness of fit of the model

Related Terms

  • Bayesian information criterion
  • Bonferroni point

Examples of Akaike information criterion in the following topics:

  • Stepwise Regression

    • Usually, this takes the form of a sequence of $F$-tests; however, other techniques are possible, such as $t$-tests, adjusted $R$-square, Akaike information criterion, Bayesian information criterion, Mallows's $C_p$, or false discovery rate.
    • Forward selection involves starting with no variables in the model, testing the addition of each variable using a chosen model comparison criterion, adding the variable (if any) that improves the model the most, and repeating this process until none improves the model.
    • Backward elimination involves starting with all candidate variables, testing the deletion of each variable using a chosen model comparison criterion, deleting the variable (if any) that improves the model the most by being deleted, and repeating this process until no further improvement is possible.
    • This problem can be mitigated if the criterion for adding (or deleting) a variable is stiff enough.
  • Grading Students

    • Even in their basic "evaluative" capacity grades can be rich sources of information for students and educators alike.
    • An essay, for example, which was characterized by very clear prose might receive an "A" for that criterion.
    • If that same essay, however, was deeply unoriginal, it might receive a "C" for that criterion.
    • And if it lacked documentation all together, it might receive a "D" or an "F" for that criterion.
    • (She might weigh each criterion equally, or might assign the most important relatively more weight).
  • Concavity and the Second Derivative Test

    • The second derivative test is a criterion for determining whether a given critical point is a local maximum or a local minimum.
    • In calculus, the second derivative test is a criterion for determining whether a given critical point of a real function of one variable is a local maximum or a local minimum using the value of the second derivative at the point.
    • It does not, however, provide information about inflection points.
  • Statistical Power

    • The Statistical Significance Criterion Used in the Test: A significance criterion is a statement of how unlikely a positive result must be, if the null hypothesis of no effect is true, for the null hypothesis to be rejected.
    • One easy way to increase the power of a test is to carry out a less conservative test by using a larger significance criterion, for example 0.10 instead of 0.05.
    • An unstandardized (direct) effect size will rarely be sufficient to determine the power, as it does not contain information about the variability in the measurements.
    • Let's say we look for a significance criterion of 0.05.
  • Introduction to Multiple Regression

    • In simple linear regression, a criterion variable is predicted from one predictor variable.
    • In multiple regression, the criterion is predicted by two or more variables.
    • In multiple regression, it is often informative to partition the sums of squares explained among the predictor variables.
    • Specifically, they are the differences between the actual scores on the criterion and the predicted scores.
    • It is assumed that the relationship between each predictor variable and the criterion variable is linear.
  • Defining conditional probability

    • It is useful to think of the condition as information we know to be true, and this information usually can be described as a known outcome or event.
    • Suppose we were provided only the information in Table 2.13 on the preceding page, i.e. only probability data.
    • Then if we took a sample of 1000 people, we would anticipate about 47% or 0.47 × 1000 = 470 would meet our information criterion.
    • Similarly, we would expect about 28% or 0.28 × 1000 = 280 to meet both the information criterion and represent our outcome of interest.
    • The complement still appears to work when conditioning on the same information.
  • Criteria to evaluate alternatives

    • The Pareto efficiency criterion fails to justify choices that result in the highest valued use of resources (economic efficiency).
    • To remedy this problem the criterion of Pareto Potential is used.
    • This example also illustrates the issue that the status quo tends to be supported by the Pareto Optimality criterion.
    • In an ideal world, informed individuals engaged in voluntary exchanges will result in transfers of property rights that are Pareto improvements and lead to economic efficiency.
  • Location, location, location

    • Where a node or a relation is drawn in the space is essentially arbitrary -- the full information about the network is contained in its list of nodes and relations.
    • Figure 4.6 shows the same graph using Layout>Circle, and selecting the "generalist-specialist" (i.e. the circle or square node type) as the organizing criterion.
    • In the current example, we've also selected the optional "node repulsion" criterion that creates separation between objects that would otherwise be located very close to one another.
    • We've also used the optional criterion of seeking to make the paths of "equal edge length" so that the distances between adjacent objects are similar.
  • Classifying Abnormal Behavior: The DSM

    • The initial impetus for developing a classification of mental disorders in the United States was the need to collect statistical information.
    • In this version, a clinical significance criterion was added to almost half of all the categories.
    • This criterion required that symptoms cause "clinically significant distress or impairment in social, occupational, or other important areas of functioning."
    • Notable changes include the change from autism and Asperger syndrome to a combined autism spectrum disorder; dropping the subtype classifications for variant forms of schizophrenia; dropping the "bereavement exclusion" for depressive disorders; a revised treatment and naming of gender-identity disorder to gender dysphoria; and changes to the criterion for post-traumatic stress disorder (PTSD).
  • CONCOR

    • For illustration, we have asked CONCOR to show us the groups that best satisfy this property when we believe that there are four groups in the Knoke information data.
    • This might be regarded as OK, but is hardly a wonderful fit (there is no real criterion for what is a good fit).
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