scholarly journals A Comparison of the Optimal Classification Rule and Maximum Likelihood Rule for Binary Variables

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
I. Egbo ◽  
S. I. Onyeagu ◽  
D. D. Ekezie ◽  
Uzoma Peter O.
Keyword(s):  
Maximum Likelihood ◽  
Classification Rule ◽  
Binary Variables ◽  
Optimal Classification

scholarly journals Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Epaminondas Markos Valsamis ◽  
Henry Husband ◽  
Gareth Ka-Wai Chan
Keyword(s):  
Time Series ◽  
Hip Fracture ◽  
Maximum Likelihood ◽  
Mortality Rate ◽  
Linear Regression ◽  
Modelling Technique ◽  
Binary Variables ◽  
Regression Modelling ◽  
Before And After ◽  
Linear Sections

Introduction. In healthcare, change is usually detected by statistical techniques comparing outcomes before and after an intervention. A common problem faced by researchers is distinguishing change due to secular trends from change due to an intervention. Interrupted time-series analysis has been shown to be effective in describing trends in retrospective time-series and in detecting change, but methods are often biased towards the point of the intervention. Binary outcomes are typically modelled by logistic regression where the log-odds of the binary event is expressed as a function of covariates such as time, making model parameters difficult to interpret. The aim of this study was to present a technique that directly models the probability of binary events to describe change patterns using linear sections. Methods. We describe a modelling method that fits progressively more complex linear sections to the time-series of binary variables. Model fitting uses maximum likelihood optimisation and models are compared for goodness of fit using Akaike’s Information Criterion. The best model describes the most likely change scenario. We applied this modelling technique to evaluate hip fracture patient mortality rate for a total of 2777 patients over a 6-year period, before and after the introduction of a dedicated hip fracture unit (HFU) at a Level 1, Major Trauma Centre. Results. The proposed modelling technique revealed time-dependent trends that explained how the implementation of the HFU influenced mortality rate in patients sustaining proximal femoral fragility fractures. The technique allowed modelling of the entire time-series without bias to the point of intervention. Modelling the binary variable of interest directly, as opposed to a transformed variable, improved the interpretability of the results. Conclusion. The proposed segmented linear regression modelling technique using maximum likelihood estimation can be employed to effectively detect trends in time-series of binary variables in retrospective studies.

scholarly journals Performance of Robust Linear Classifier with Multivariate Binary Variables

2015 ◽  
Vol 7 (4) ◽  
pp. 104
Author(s):  
I. Egbo ◽  
M. Egbo ◽  
S. I. Onyeagu
Keyword(s):  
Maximum Likelihood ◽  
Discriminant Function ◽  
Likelihood Function ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Data Set ◽  
Binary Variables ◽  
Linear Discriminant ◽  
Linear Classifiers ◽  
Fisher’S Linear Discriminant

<p>This paper focuses on the robust classification procedures in two group discriminant analysis with multivariate binary variables. A normal distribution based data set is generated using the R-software statistical analysis system 2.15.3 using Barlett’s approximation to chi-square, the data set was found to be homogenous and was subjected to five linear classifiers namely: maximum likelihood discriminant function, fisher’s linear discriminant function, likelihood ratio function, full multinomial function and nearest neighbour function rule. To judge the performance of these procedures, the apparent error rates for each procedure are obtained for different sample sizes. The results obtained ranked the procedures as follows: fisher’s linear discriminant function, maximum likelihood, full multinomial, likelihood function and nearest neigbour function.</p>

scholarly journals Error rate control for classification rules in multiclass mixture models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tristan Mary-Huard ◽  
Vittorio Perduca ◽  
Marie-Laure Martin-Magniette ◽  
Gilles Blanchard
Keyword(s):  
Mixture Models ◽  
Error Rate ◽  
Classification Rule ◽  
Misclassification Rate ◽  
Classification Error ◽  
Type I ◽  
Type Ii ◽  
Optimal Rule ◽  
Optimal Region ◽  
Optimal Classification

Abstract In the context of finite mixture models one considers the problem of classifying as many observations as possible in the classes of interest while controlling the classification error rate in these same classes. Similar to what is done in the framework of statistical test theory, different type I and type II-like classification error rates can be defined, along with their associated optimal rules, where optimality is defined as minimizing type II error rate while controlling type I error rate at some nominal level. It is first shown that finding an optimal classification rule boils down to searching an optimal region in the observation space where to apply the classical Maximum A Posteriori (MAP) rule. Depending on the misclassification rate to be controlled, the shape of the optimal region is provided, along with a heuristic to compute the optimal classification rule in practice. In particular, a multiclass FDR-like optimal rule is defined and compared to the thresholded MAP rules that is used in most applications. It is shown on both simulated and real datasets that the FDR-like optimal rule may be significantly less conservative than the thresholded MAP rule.

Maximum Likelihood for Social Science

2018 ◽  
Author(s):  
Michael D. Ward ◽  
John S. Ahlquist
Keyword(s):  
Maximum Likelihood ◽  
Social Science
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