An IO–Modification of Potential Method (Coimbatore 2008) (slides) (text)
In this paper we are performing some modification of Potential Method so that it can be recognize as an Input-Output method. This approach is tested on the ’Japan City Banks’ example taken from Cooper & all. where authors ... are using Data Envelopment Analysis (DEA) approach. It is known that DEA is not capable to distinguish ’efficient’ DMUs’ (Decision Making Units) among themselves. In our approach this is not the case — we obtain the ranking od all units in consideration.In DEA the weighted efficiency of a Decision Making Unit (DMU) is expressed as a fraction of arithmetic mean of inputs divided by arithmetic mean of outputs where inputs and outputs have, in general, different weights. In this paper we are going to present a new approach where arithmetic mean is replaced by geometric mean. This approach is a modified Potential Method (PM) which use preference graph as an input rather than a pairwise comparison matrix. We shall say a few words about PM and compare the results of both methods, DEA and PM, on an interesting example.
Analysis of effective motivational indicators among members on entry in agricultural cooperatives (ISCCRO 2016) (slides)
(With Aleksandar Nedanov and Vladimir Jerebić)This study presents analysis of effective motivation factors among members on entry in agricultural cooperatives based on the field research with sample size of 202 members. Using correspondence analysis (CA) as a multivariate statistical method for visualisation of categorical data we discovered a pattern of association between motivational factors. Motivational factors are divided into... two groups of social and economic factors while economic factors such as safe product placement and production cost reduction proved to be the most important motivation factor on entry in agricultural cooperatives.
Further, we recoded data using the recording scheme "doubling of ratings" and showed how ranking of economical motivational factors depends on type of membership, production sector, duration of participation in agricultural production or levels of revenue.
Respondents with full ownership rights who work in agricultural production less than five years and achieved small amount of incomes from their production are more inclined for choosing a better market positioning for their agricultural product.
Respondents with higher amount of income from agricultural production or business collaboration with the cooperatives are more likely to choose reducing costs for their own production, unlike the respondents with less amount of income who like to prefer better market positioning for their product. Inside the group of social motives, the opportunities for developing professional skills and exchanging useful information among members received the highest score from each respondent. However, on the level of all motivational indicators with all other social indicators does not have an important significance for entering the cooperative.
Cumulative Prospect Evaluation with Moving Reference Point (ISCCRO 2016) (slides)
(With Doris Božinović)Prospect is a lottery with the reference point which may be evaluated according to the Cumulative Prospect Theory using the ideas of Quiggin (1982) and Yari (1986). If the prospect is a time series, this approach is questionable because there is not obvious how to choose the reference point and... moreover, the probabilities of the lottery are unknown. One idea is to introduce 'dynamical referencing' by changing the reference point along the time series.
The first step is to make a prospect from time series as a sequence of consecutive gains (looses) which are categorized, and the corresponding probabilities are the probabilities of those category. Then we set the reference value of such lottery to zero to obtain the prospect.
As an illustration of this approach we shall compare the cumulative prospect values for the shares of the companies: IBM, Western Digital and Apple in the period from 2010/01/03 to 2011/01/03 using the probability deformation according to Prelec (1998) and the original utility given by Kahneman and Tversky (1992). Some interesting properties of the 'dynamical referencing' and simulations will be given as well.
Self Duality and Conflict Resolution (Sienna 2010) (labsit)
A mathematical model of a goal-oriented thinking with feed back is described. Basic notions: criteria, decision graph, ranking, hierarchy, duality and self-duality are introduced and explained. Mental process of conict resolution is considered and its mathematical model is made as a decision hierarchy with feedback. Some real world examples (intelligent mobile robots, risk-as-feeling hypothesis and government budget reevaluation) are solved calculating... the fixed point of the self-assessment operator.A standard approach to conict resolution is to reconsider the goals and their preferences or to add some new options or actions into consideration. In this article we suppose that decision maker exhausted all possibilities to add some other option into consideration, i.e. that he does not change the structure of the hierarchy and does not change the preferences of the objects inside the hierarchy. The source of the conict is the unknown importance of his goals.
Self-duality in a decision process arises when some objects are also criteria for themselves. A typical example of self-duality is a group of decision makers who attempt to rank themselves.
In internal conict, a decision maker reconsiders his goals from the point of view of actions. For each action there are some goals which support the action more than other actions. This means that each action have a tendency to rank the goals, directly or indirectly using some extra criteria. This means that the goals, using actions, are ranking goals. In the choice under risk, precisely in risk-as-feeling model introduced by Loewenstein (2001), people are assumed to evaluate risky alternatives at a cognitive level, based largely on the probability and desirability of associated consequences. Such cognitive evaluations have a_ective consequences, and feeling states also exert a reciprocal inuence on cognitive evaluations.
Decision Making via Potential Method (Nica 2010) (poster)
The purpose of this article is to present a new ranking method in Multicriteria Decision Making (MCDM), called Potential Method (PM), and a public domain software on URL http:/pc205.math.hr/Decision, based on this approach. PM is founded on graph theory and can be used in decision table approach as well as in hierarchically structured models, with exact data ([3]) and subjective given preferences.... In a certain way it also extends the classical approach for aggregation of individual preferences into a social preference, known as Kemeny’s median. Until now, we gave comparative study of PM with PROMETHEE method, An- alytical Hierarchy Process and Evidential Reasoning method with excellent results, as well as with complete and incomplete structure.PM approach offers several benefits: inconsistency measure of the preference flow, flow distance and easy treatment of ’missing data’. The first one measure inconsistency of the flow and equals zero if and only if the preference flow is acyclic. The second notion gives possibility to measure dissimilarity between two flows on the graphs over the same set of vertices. This is useful in group decision where inconsistency is not a valuable information for consensus flow, see [link to Graph Distance in MCDM] for details. The third benefit is evident from equation (1) because input data for PM is a flow not necessarily defined on the complete graph.
Here is a short description of PM in case of one criterion and one decision maker. For construction of consensus flow in general situation see [2]. The vertices of the graph are the alternatives under consideration. Decision process starts with pairwise comparisons of the vertices. An arc \(\alpha\) between two vertices is defined whenever they are compared with orientation towards more preferable vertex. The flow component \(F_\alpha\) is given as a preference intensity, \(F_\alpha=0\) if it’s vertices are equally preferable and orientation of the arc is arbitrary in that case. If \(B\) denotes incidence matrix of the graph then, the equation \[ B^\tau BX = B^\tau F, \sum_{i=1}^m X_i=0 \] defines a unique potential \(X : V \rightarrow \mathbb{R}\) on the set of vertices which called normal integral of \(F\) . If the graph is not connected, the normal integral is unique on each connected component of the graph. Mentioned site is still growing, and future projects are: moderated group decision and conjoint analysis in marketing research based on PM.
Asymptotic stability in network with feedback and conflict resolution (BIOSTAT 2010) (poster)
(abstract) Networks with feedback in conflict resolution context are the generalization of the hierarchical structure in goal oriented thinking. The concept of self-duality explains the situation when the elements of decision are criteria and the options at the same time.... A typical example is a group of decision makers who attempt to rank themselves (self ranking).In this paper we suppose that decision maker exhausted all possibilities to add some other option into consideration, i.e. that he does not change the structure of the hierarchy and does not change the preferences of the objects inside the hierarchy. The source of the conflict is the unknown importance of his goals. In a self ranking system the change of initial ranks w directly influences the weights of actions, and indirectly changes the weights Phi(w) of the goals because of the feedback. Repeating the process \[w\mapsto\Phi(w)\mapsto\Phi(\Phi(w))\mapsto\cdots\Phi^n(w)\mapsto\cdots\] the infinite sequence of weights is obtained. It can be proved that this sequence has a unique fixed point which is independent of the first choice of w.
An application of this approach is the conflict resolution which arise when two robots are passing through the corridor. To avoid the crash they can:
turn right (R), turn left (L), wait (no action) (W).
Early recognition of Alzheimer Disease (BIOSTAT 2014) (slides)
(With Sanja Josef Golubić)On the basis of a measurement results of the nineteen participants A1–A19 subjected to four psychological tests: Mental Status Exam (MSE), Rey-Osterrieth complex figure test (REY), Performance IQ test (IQprf), Verbal IQ test (IQver), and two Magnetoencephalography (MEG) tests: let us call them for the moment: Frq and Rare. ...
The fact is that some participants are healthy, some of them have Mild Cognitive Impairment diagnosis (MCI),which is seen as a risk factor for Alzheimer’s disease (AD) and the others seems to have AD already.
The aim of this analysis is: to find out a relationship between psychological and MEG variables, more precisely, between the categorical values: Healthy, MCI, AD, suggested by both type of variables.
The first insight to the data suggests 2 (two) clusters of the 'psychological participants' while 'MEG participants' are divided into 3 evident clusters. In both clusterizations AD-participants are correctly identified.
Three methods are tested to split non-AD 'psychological participants' into 2 clusters. (1) Brut force method, (2) Canonical Correspondence Analysis and (3) Multicriteria Decision Analysis approach. All of them suggests 3 clusters of the 'psychological participants'. The results should be clinically improved (or disapproved).
Structure Equation Model of Heptathlon (BIOSTAT 2014) (slides)
Women's heptathlon is the combined event which consists of the following events: 100 meters hurdles, High jump, Shot put, 200 meters, Long jump, Javelin throw and 800 meters. Understanding he interrelationship between the disciplines may have implications for training optimization and competition as well. ...One approach to understand this relationships can be addressed through multivariate statistical analysis, defined as structural equation modeling and path analysis (Heazlewood (2011)).
Mackenzie (2007) has attempted to assign relative conceptual weights for each event with constructs of aerobic endurance, gross strength skill, relative strength, running speed, mobility, explosive strength-power, speed endurance and strength endurance that are believed to underpin each event (motoric skills).
The template of Mackenzie is a starting point for our approach based on simple Multicriteria Decision Analysis procedures. The aim of the analysis is to use the heptathlon event results (OI London 2012) as the measurement process for the motoric skills, and to suggest eventually a new scoring system which is different from the current IAAF system.
Statistical Analysis of the Cognitive Domain Taxonomy Table (BIOSTAT 2017) (slides)
Taxonomy table of the cognitive domain has 4 categories for knowledge and 6 categories for processes. The complexity value of the cell in that table depends upon the 'distance' from the left upper corner. Our idea is to calculate this complexity value using the contingency table obtained in the following way, ... in fact there are several ways to do that. We asked each student of the course in Game Theory to evaluate his own knowledge (a day before the exam) on the taxonomy table (TT) by putting a point in one or several cells of the table.Correspondence Analysis (CA) of that contingency table gave a strong nonlinear association which was again analysed by the Detrended CA (DCA). The final result is that the association is one dimensional which gives rise to some interesting questions about the validity of the proposed taxonomy.
Furthermore, the scores obtained by DCA may be used to generate the metric of the TT which evaluates each cell of the table. This metric may be used to evaluate the students abilities and outcomes. Further experiments and analysis have to be done.
Preference Measurement and Application to Choice Theory (BIOSTAT 2019) (aka Network Choice Theory) (slides)
The problem of single choice repetition from the finite set of objects {A, B, C, …} has a long story. The classical choice theory, binomial and multinomial, are based on the random utility which captures the uncertainty of choosing one object among offered two or all of them. This theory depends upon the choice axiom of Luce (1959) which ... asserts that the probability of choosing an element does not depend upon the context of choosing. Network choice theory describes what happens when this axiom is not satisfied.The simplest version of the individual choice network model represents the objects as the nodes in the graph and the oriented edges capture the frequency of choosing the elements from the offered pair. For instance, if A:B = 3:2 is the relative ratio of probabilities of choosing A and B when {A,B} is offered, this ratio generates a multi-graph with parallel edges: one from B to A with weight 3, and the other one from A to B with weight 2. The situation may be more complicated if the ratios of A:B:C or A:B:C:D are offered. Even in the case of sparse network the probability distribution may be calculated.
Potential method (PM), developed by the author, gives the probability of choosing each element after solving Laplace equation of the given graph. The graph is consistent if and only if the axiom of Luce is satisfied. Some examples of the choice network will be presented and solved by the PM-software.
Group networks may be analysed by cluster analysis after defining a suitable distance of the individual networks.
Possible applications, with a little modifications, are: consumption, survey analysis, social sciences.
Sparse potpensity method (BIOSTAT 2019) (slides)
Propensity scoring is a well known approach for calculating the treatment effect in controlled and observed experiments based on Logistic Regression (LR). Here we investigate a possibility of using the Potential Method (PM) as a base method for scale construction before matching.A testing example is lalonde (dataset from the R-package Matching), ... an observational data with 297 treated and 15992 controlled items. The idea is to make approximative matching (using treated items profiles), to construct some scale (potential) and in the second stage to make matching (hungarian algorithm) using this scale instead of items profiles. In the second stage a few of the treated items are also removed from the table.
The second phase matching is done on each strata and the overall effect is calculated after that. Some strata effect is negative which needs some social explanations, but the overall effect is even higher then the same one calculated using propensity score with different matching algorithm.
The sparse potpensity matching works in the same way. In the first step the approximative matching is done without exact matching and the potential scoring works with incomplete data as well.