Higher Order Effects in Log-Linear and Log-Non-Linear Models for Contingency Tables with Ordered Categories

Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fitting and re-fitting to search for the best model. Another advantage is that quadratic and higher order effects can readily be included, in contrast to conventional log-linear models which incorporate linear terms only.The focus of the discussion is the application of the new parameter estimation technique to multi-way contingency tables with at least one ordered variable. This will also be done by considering singly and doubly ordered two-way contingency tables. It will be shown by example that the resulting parameter estimates are numerically similar to corresponding maximum likelihood estimates for ordinal log-linear models.

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Time after time: support for memory accounts of temporal preparation.

10.31234/osf.io/5t8b7 ◽

2019 ◽

Author(s):

Joe Butler ◽

Samuel Ngabo ◽

Marcus Missal

Keyword(s):

Response Times ◽

Reaction Times ◽

Evidence Base ◽

Higher Order ◽

Order Effects ◽

Previous Trial ◽

Adaptive Responses ◽

Temporal Preparation ◽

Subsequent Trial ◽

Higher Order Effects

Complex biological systems build up temporal expectations to facilitate adaptive responses to environmental events, in order to minimise costs associated with incorrect responses, and maximise the benefits of correct responses. In the lab, this is clearly demonstrated in tasks which show faster response times when the period between warning (S1) and target stimulus (S2) on the previous trial was short and slower when the previous trial foreperiod was long. The mechanisms driving such higher order effects in temporal preparation paradigms are still under debate, with key theories proposing that either i) the foreperiod leads to automatic modulation of the arousal system which influences responses on the subsequent trial, or ii) that exposure to a foreperiod results in the creation of a memory trace which is used to guide responses on the subsequent trial. Here we provide data which extends the evidence base for the memory accounts, by showing that previous foreperiod exposures are cumulative with reaction times shortening after repeated exposures; whilst also demonstrate that the higher order effects associated with a foreperiod remain active for several trials.

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Higher-order effects in the dynamics of hierarchical triple systems: Quadrupole-squared terms

Physical Review D ◽

10.1103/physrevd.103.063003 ◽

2021 ◽

Vol 103 (6) ◽

Author(s):

Clifford M. Will

Keyword(s):

Higher Order ◽

Order Effects ◽

Triple Systems ◽

Higher Order Effects

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Responsible innovation, anticipation and responsiveness: case studies of algorithms in decision support in justice and security, and an exploration of potential, unintended, undesirable, higher-order effects

AI and Ethics ◽

10.1007/s43681-021-00063-2 ◽

2021 ◽

Author(s):

Marc Steen ◽

Tjerk Timan ◽

Ibo van de Poel

Keyword(s):

Decision Support ◽

Case Studies ◽

Personal Data ◽

Higher Order ◽

Popular Media ◽

Responsible Innovation ◽

Order Effects ◽

Key Dimensions ◽

Higher Order Effects

AbstractThe collection and use of personal data on citizens in the design and deployment of algorithms in the domain of justice and security is a sensitive topic. Values like fairness, autonomy, privacy, accuracy, transparency and property are at stake. Negative examples of algorithms that propagate or exacerbate biases, inequalities or injustices have received ample attention, both in academia and in popular media. To supplement this view, we will discuss two positive examples of Responsible Innovation (RI): the design and deployment of algorithms in decision support, with good intentions and careful approaches. We then explore potential, unintended, undesirable, higher-order effects of algorithms—effects that may occur despite good intentions and careful approaches. We do that by engaging with anticipation and responsiveness, two key dimensions of Responsible Innovation. We close the paper with proposing a framework and a series of tentative recommendations to promote anticipation and responsiveness in the design and deployment of algorithms in decision support in the domain of justice and security.

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