Single-Variable Threshold Effects in Ordered Response Models With an Application to Estimating the Income-Happiness Gradient

2016 ◽  
Vol 34 (1) ◽  
pp. 42-52
Author(s):  
Andrew Hodge ◽  
Sriram Shankar
Keyword(s):  
Threshold Effects ◽  
Single Variable ◽  
Response Models ◽  
Variable Threshold ◽  
Ordered Response

Modified Mixed Generalized Ordered Response Model to Handle Misclassification in Injury Severity Data

2018 ◽  
Vol 2672 (30) ◽  
pp. 53-63 ◽  
Author(s):  
Lacramioara Balan ◽  
Rajesh Paleti
Keyword(s):  
Injury Severity ◽  
Random Variable ◽  
Parameter Estimates ◽  
Discrete Random Variable ◽  
Response Models ◽  
Ordinal Response ◽  
Proposed Model ◽  
Misclassification Errors ◽  
Misclassification Rates ◽  
Ordered Response

Traditional crash databases that record police-reported injury severity data are prone to misclassification errors. Ignoring these errors in discrete ordered response models used for analyzing injury severity can lead to biased and inconsistent parameter estimates. In this study, a mixed generalized ordered response (MGOR) model that quantifies misclassification rates in the injury severity variable and adjusts the bias in parameter estimates associated with misclassification was developed. The proposed model does this by considering the observed injury severity outcome as a realization from a discrete random variable that depends on true latent injury severity that is unobservable to the analyst. The model was used to analyze misclassification rates in police-reported injury severity in the 2014 General Estimates System (GES) data. The model found that only 68.23% and 62.75% of possible and non-incapacitating injuries were correctly recorded in the GES data. Moreover, comparative analysis with the MGOR model that ignores misclassification not only has lower data fit but also considerable bias in both the parameter and elasticity estimates. The model developed in this study can be used to analyze misclassification errors in ordinal response variables in other empirical contexts.

scholarly journals Ordered Response Models

2007 ◽  
pp. 167-181 ◽  
Author(s):  
Stefan Boes ◽  
Rainer Winkelmann
Keyword(s):  
Response Models ◽  
Ordered Response

Non-decreasing threshold variances in mixed generalized ordered response models: A negative correlations approach to variance reduction

2018 ◽  
Vol 20 ◽  
pp. 46-67 ◽  
Author(s):  
Suryaprasanna Kumar Balusu ◽  
Abdul Rawoof Pinjari ◽  
Fred L. Mannering ◽  
Naveen Eluru
Keyword(s):  
Variance Reduction ◽  
Response Models ◽  
Ordered Response

scholarly journals Reduction of the Hodgkin-Huxley Equations to a Single-Variable Threshold Model

1997 ◽  
Vol 9 (5) ◽  
pp. 1015-1045 ◽  
Author(s):  
Werner M. Kistler ◽  
Wulfram Gerstner ◽  
J. Leo van Hemmen
Keyword(s):  
Threshold Model ◽  
Order Term ◽  
Model Neuron ◽  
Membrane Voltage ◽  
Single Variable ◽  
Threshold Element ◽  
Variable Threshold ◽  
First Order ◽  
Output Spike ◽  
Order Kernel

It is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential. Higher-order kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion, the kernels depend on the firing time of the most recent output spike. In particular, a zero-order kernel that describes the shape of the spike and the typical after-potential is included. Our model neuron fires if the membrane voltage, given by the truncated response kernel expansion, crosses a threshold. The threshold model is tested on a spike train generated by the Hodgkin-Huxley model with a stochastic input current. We find that the threshold model predicts 90 percent of the spikes correctly. Our results show that, to good approximation, the description of a neuron as a threshold element can indeed be justified.

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