scholarly journals A Framework for Evaluating Pairwise and Multiway Synchrony Among Stimulus-Driven Neurons

2012 ◽  
Vol 24 (8) ◽  
pp. 2007-2032 ◽  
Author(s):  
Ryan C. Kelly ◽  
Robert E. Kass
Keyword(s):  
Linear Models ◽  
Neuron Activity ◽  
Linear Modeling ◽  
Maximum Entropy Models ◽  
Synchronous Interaction ◽  
History Effects ◽  
Covariate Effects ◽  
Modeling Techniques ◽  
Spike Train Data ◽  
Log Linear

Several authors have previously discussed the use of log-linear models, often called maximum entropy models, for analyzing spike train data to detect synchrony. The usual log-linear modeling techniques, however, do not allow time-varying firing rates that typically appear in stimulus-driven (or action-driven) neurons, nor do they incorporate non-Poisson history effects or covariate effects. We generalize the usual approach, combining point-process regression models of individual neuron activity with log-linear models of multiway synchronous interaction. The methods are illustrated with results found in spike trains recorded simultaneously from primary visual cortex. We then assess the amount of data needed to reliably detect multiway spiking.

Confirmatory Analysis of Aggregate Hierarchical Market Structures: Inferences from Brand-Switching Behavior

1989 ◽  
Vol 26 (4) ◽  
pp. 444-453 ◽  
Author(s):  
Ajith Kumar ◽  
C. M. Sashi
Keyword(s):  
Directed Graph ◽  
Probabilistic Model ◽  
Switching Behavior ◽  
Aggregate Level ◽  
Linear Modeling ◽  
Market Structures ◽  
Brand Switching ◽  
Modeling Techniques ◽  
Confirmatory Analysis ◽  
Log Linear

A probabilistic model is developed for testing hypothesized hierarchical market structures at the aggregate level using brand-switching data. Each hypothesized structure is represented by a directed graph and its parameters are estimated by using log-linear modeling techniques. As an illustration, the method is applied to data on soft drinks.

scholarly journals A non-iterative alternative to ordinal Log-Linear models

2004 ◽  
Vol 8 (2) ◽  
pp. 67-86 ◽  
Author(s):  
Eric J. Beh ◽  
Pamela J. Davy
Keyword(s):  
Maximum Likelihood ◽  
Linear Models ◽  
Contingency Tables ◽  
Model Fitting ◽  
Maximum Likelihood Estimates ◽  
Order Effects ◽  
Parameter Estimates ◽  
Linear Modeling ◽  
Statistical Tool ◽  
Log Linear

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.

scholarly journals Sensitivity of Population Size Estimation for Violating Parametric Assumptions in Log-linear Models

2015 ◽  
Vol 31 (3) ◽  
pp. 357-379 ◽  
Author(s):  
Susanna C. Gerritse ◽  
Peter G.M. van der Heijden ◽  
Bart F.M. Bakker
Keyword(s):  
Population Size ◽  
Linear Models ◽  
General Setting ◽  
Sensitivity Analyses ◽  
Size Estimation ◽  
Linear Modeling ◽  
Population Size Estimate ◽  
Size Estimate ◽  
Important Quality ◽  
Log Linear

Abstract An important quality aspect of censuses is the degree of coverage of the population. When administrative registers are available undercoverage can be estimated via capture-recapture methodology. The standard approach uses the log-linear model that relies on the assumption that being in the first register is independent of being in the second register. In models using covariates, this assumption of independence is relaxed into independence conditional on covariates. In this article we describe, in a general setting, how sensitivity analyses can be carried out to assess the robustness of the population size estimate. We make use of log-linear Poisson regression using an offset, to simulate departure from the model. This approach can be extended to the case where we have covariates observed in both registers, and to a model with covariates observed in only one register. The robustness of the population size estimate is a function of implied coverage: as implied coverage is low the robustness is low. We conclude that it is important for researchers to investigate and report the estimated robustness of their population size estimate for quality reasons. Extensions are made to log-linear modeling in case of more than two registers and the multiplier method

An Assessment of the Contribution of log Linear Models to Marketing Research

1981 ◽  
Vol 45 (2) ◽  
pp. 89-97 ◽  
Author(s):  
Robert C. Blattberg ◽  
Robert J. Dolan
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Recent Literature ◽  
Contingency Tables ◽  
Marketing Research ◽  
Ordinary Least Squares ◽  
Linear Modeling ◽  
Log Linear ◽  
Model Structures

Recent literature contains several expositions of the log-linear modeling (LLM) capability of analyzing multiway contingency tables. This method has been proposed as a way of overcoming the deficiencies of traditional models such as ordinary least squares and AID. In order to begin an assessment of the utility of LLM, we report the results of four applications, and then provide a rationale for these empirical findings by examining the different model structures.

Neural Coding: Higher-Order Temporal Patterns in the Neurostatistics of Cell Assemblies

2000 ◽  
Vol 12 (11) ◽  
pp. 2621-2653 ◽  
Author(s):  
Laura Martignon ◽  
Gustavo Deco ◽  
Kathryn Laskey ◽  
Mathew Diamond ◽  
Winrich Freiwald ◽  
...  
Keyword(s):  
Experimental Data ◽  
Spike Train ◽  
Neural Coding ◽  
Linear Models ◽  
Temporal Patterns ◽  
Higher Order ◽  
Neural Activation ◽  
Spike Train Data ◽  
Behaving Monkeys ◽  
Log Linear

Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data. We mention three possible measures for the presence of higher-order patterns of neural activation—coefficients of log-linear models, connected cumulants, and redundancies—and present arguments in favor of the coefficients of log-linear models. We present test statistics for detecting the presence of higher-order interactions in spike train data by parameterizing these interactions in terms of coefficients of log-linear models. We also present a Bayesian approach for inferring the existence or absence of interactions and estimating their strength. The two methods, the frequentist and the Bayesian one, are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other. A heuristic for the analysis of temporal patterns is also proposed. Finally, a Bayesian test is presented that establishes stochastic differences between recorded segments of data. The methods are applied to experimental data and synthetic data drawn from our statistical models. Our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys, the somatosensory cortex of anesthetized rats, and multiunit recordings in the visual cortex of behaving monkeys.

When and why are log-linear models self-normalizing?

2015 ◽  
Author(s):  
Jacob Andreas ◽  
Dan Klein
Keyword(s):  
Linear Models ◽  
Log Linear

Log-Linear Models with Dependent Spatial Data

1983 ◽  
Vol 15 (6) ◽  
pp. 801-813 ◽  
Author(s):  
B Fingleton
Keyword(s):  
Spatial Data ◽  
Statistical Models ◽  
Linear Models ◽  
Square Lattice ◽  
Categorical Variables ◽  
Systematic Sampling ◽  
Pairwise Correlations ◽  
Independent Observations ◽  
Intersection Points ◽  
Log Linear

Log-linear models are an appropriate means of determining the magnitude and direction of interactions between categorical variables that in common with other statistical models assume independent observations. Spatial data are often dependent rather than independent and thus the analysis of spatial data by log-linear models may erroneously detect interactions between variables that are spurious and are the consequence of pairwise correlations between observations. A procedure is described in this paper to accommodate these effects that requires only very minimal assumptions about the nature of the autocorrelation process given systematic sampling at intersection points on a square lattice.

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