### Abstract

A monotonic state-trace implies that a single latent factor is sufficient to explain the joint variation between two outcome variables across a set of conditions. There are, however, few methods available for assessing how much evidence a sample of data provides about whether the variables are truly monotonically related or not. We present a model that estimates the statistic Mˆ which reflects the amount of evidence a dataset provides about whether two or more outcome variables are jointly monotonically related at the group level. This statistic is based on modeling the covariation between outcome measures in terms of a kernel function, which allows for computation of the latent derivatives of each outcome variable with respect to the other. We then compare the prior and posterior probabilities that these derivatives are all of the same sign (and are thus monotonic) to obtain Mˆ. Simulations show that Mˆ discriminates between monotonic and non-monotonic state traces and an example illustrates how the model can be applied to both continuous and binomial data from between-subjects, within-subjects, or mixed designs.

Original language | English (US) |
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Journal | Journal of Mathematical Psychology |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Bayesian statistics
- Gaussian processes
- State-trace analysis

### ASJC Scopus subject areas

- Psychology(all)
- Applied Mathematics

### Cite this

**Dial Mˆ for monotonic : A kernel-based Bayesian approach to state-trace analysis.** / Cox, Gregory E.; Kalish, Michael L.

Research output: Contribution to journal › Review article

}

TY - JOUR

T1 - Dial Mˆ for monotonic

T2 - A kernel-based Bayesian approach to state-trace analysis

AU - Cox, Gregory E.

AU - Kalish, Michael L

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A monotonic state-trace implies that a single latent factor is sufficient to explain the joint variation between two outcome variables across a set of conditions. There are, however, few methods available for assessing how much evidence a sample of data provides about whether the variables are truly monotonically related or not. We present a model that estimates the statistic Mˆ which reflects the amount of evidence a dataset provides about whether two or more outcome variables are jointly monotonically related at the group level. This statistic is based on modeling the covariation between outcome measures in terms of a kernel function, which allows for computation of the latent derivatives of each outcome variable with respect to the other. We then compare the prior and posterior probabilities that these derivatives are all of the same sign (and are thus monotonic) to obtain Mˆ. Simulations show that Mˆ discriminates between monotonic and non-monotonic state traces and an example illustrates how the model can be applied to both continuous and binomial data from between-subjects, within-subjects, or mixed designs.

AB - A monotonic state-trace implies that a single latent factor is sufficient to explain the joint variation between two outcome variables across a set of conditions. There are, however, few methods available for assessing how much evidence a sample of data provides about whether the variables are truly monotonically related or not. We present a model that estimates the statistic Mˆ which reflects the amount of evidence a dataset provides about whether two or more outcome variables are jointly monotonically related at the group level. This statistic is based on modeling the covariation between outcome measures in terms of a kernel function, which allows for computation of the latent derivatives of each outcome variable with respect to the other. We then compare the prior and posterior probabilities that these derivatives are all of the same sign (and are thus monotonic) to obtain Mˆ. Simulations show that Mˆ discriminates between monotonic and non-monotonic state traces and an example illustrates how the model can be applied to both continuous and binomial data from between-subjects, within-subjects, or mixed designs.

KW - Bayesian statistics

KW - Gaussian processes

KW - State-trace analysis

UR - http://www.scopus.com/inward/record.url?scp=85062144550&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062144550&partnerID=8YFLogxK

U2 - 10.1016/j.jmp.2019.02.002

DO - 10.1016/j.jmp.2019.02.002

M3 - Review article

AN - SCOPUS:85062144550

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

ER -