In standard econometric application all variables are analyzed statistically before being used in mathematical models. In this framework we considered nonstationary distribution as an starting procedure on the study of consumer behavior in a local market area whereof nonhomogeneity of buyers and small size effect could be present. By evaluation of the degree of nonstationary of the actual state for particular variable as observed, we hope to be able to estimate and interpret the model outcomes. Assuming the nonstationary of variables as indicator of the overall stet itself, we argue that the state where observation were made is nonstationary too, and for that reason, models are expected to not fit well. In the other hand, by dropping the significance level in model fitting process we expect to count for this instability whereas the model remains valid. Herewith, the logistic model for consumer behavior in our system is applied and calculated using significance level 0.850.90. Under such limiting constraint assumption we identified the variables that mostly affected the proportion between expense categories and the characteristics of the expenses that mostly describe the market consumer behavior in the unity studied. We hope that methodically this procedure could be helpful for other similar market or sociometric study as well.
Consumer behavior is a key element in understanding market dynamics and marketing itself. It refers to those actions and related activities of persons involved specifically in buying and using economic goods and services [
We realized the survey in Vlore district, a seaside city in south west of Albania. The city has no specific characteristics in the sense of economical level, ethnic cultures etc., one could assume with no doubt as practically representative for all urban area of the country, hence no additional variables are expected to interfere in the system [
Table 1:Predictor Variables
Predictor Variables  Value  
X1  Variable  Type  set I  Set II 
X2  Family type  categorical  15  15 
X3  Education level  categorical  15  14 
X4  Age  categorical  16  14 
X5  Employment Status  categorical  13  12 
X6  Income Type  categorical  13  19 
X7  Gender  categorical  12  12 
X8  Total Budged  numerical  Real  Real 
Indicators or response variables have been considered in two approaches. First we use the proportion of the expenses for each type of expenditure in the role of the probability that consumer would spend its own budget in this type of commodity. Next, we change them to the categorical representation assuming that the behavior of the consumer is driven from the decision to pay in a specific range for specific goods needed. To avoid over detailed profile of the consumer, the data gathered from the inquiry were reorganized to form 4 distinct variables respectively the expenses for basic goods and services, common expenditure, life quality expenses and luxury expenses. This reduction is supported by factorial analysis too..
Reorganizing the data i frequencies and getting distribution from optimized histograms as recommended in [
which in the limit q1 reproduce the Gaussians and lognormal respectively [ 3],[ 5]
According to such detailed view this will happen when additive or multiplicative properties turn to be dominant as detailed for other systems in [ 5] and acknowledged as Tsallis statistics In this approach if the distribution is stationary and otherwise it is not Moreover, in the interval distribution has infinite variance whereas for q in the interval the distribution still exists but the variance is indefinite [ 3] Above q= 3 there is no distribution Remember that those (Tsallis) conditions in q correspond to the Levy stability as seen from the relationship [ 3] Letting aside the nature of processes governing such system, but using conclusions for nonstationary states and practical estimation of it as briefed above, we apply directly relations (1) to fit distributions of data series for variables Considering the fact that number of individuals interviewed (number of valid observation) is small (N= 3 50), the histogram optimization has been considered with great care according to Scot and FreidmanDiaconics rule as discussed in [ 19] We applied a tuning technique as proposed in [ 18] around the bin size found in standard procedures We observe that q parameter is obtained in the range [1 329] and all variables except one have q> 5/ 3 and therefore distributions are nonstationary An immediate finding is that the average values of variables do not represent the series if strictly statistically speaking For some of them, the statistical variance is infinite or even indefinite according to [ 3], [ 5] But the most important is the finding that some of them have not distribution at all as the 1 parameter is 3 or more We excluded this variable as highly disturbed From the other side, we obtained that many variables have indefinite variance and therefore those are inappropriate to be included in models because they miss an important statistical characterizes the second moment In the Figure 1 we showed those distributions in loglog graph to better emphasize the visual differences of the distributions
Moreover we observe that if one select subclasses belonging to a fixed categorical value, the number of such sampler become smaller than the minimum size requested to proceed with statistical analysis. Therefore considering a specific variable for example “luxury expenses” we should filter families with many children that have no more than one parent employed; families that are not having their incomes limited to the pensions or other social care etc., that by definition are not subject of discussion what to do on luxury expenses because they have predefined choice, no budget in this disposal. Doing so the sampler size became abnormally small to work with, hence we should work with all values of cause variables included. We have a preliminary result that either non stable per se, or nonstable caused from nonoptimal observation the series are nonstationary or the average values are not representative.
Table 4 Evidences for the stability of the distribution for predictor variables and FA analysis
Qstat  E[Y]  Qvariance  
Y1  1.7265  0.2834  Infinite  
Y2  2.9705  0.0088  indefinite  
Y3  1.7351  0.0891  indefinite  
Y4  1.3925  0.0353  finite  
Y5  1.4295  0.0568  finite  
Y6  1.7756  0.0423  Infinite  
Y7  1.9281  0.0402  Infinite  
Y8  2.0907  0.022  Indefinite  
Y9  2.0836  0.104  indefinite  
Y10  2.0403  0.1142  indefinite  
Y11  1.8831  0.005  Infinite  
Y12  1.9333  0.005  Infinite 
Therefore, the set of observations of expenditures for specific goods or services and their proportion fail to represent the profile of consumers system analyzed (or generalized consumer characteristics. This result told us that either these are inappropriate for the system or the measurements are far from the homogenized consumer medium. Considering that some of variables are less stationary than others, there is logic move to check which of them could be removed or transformed to make the model fits better. Therefore factorial analysis has been performed to check the idea of reducing analytically the number of variables. We identify that from 12 variables of the profile 5 of them express more than 92% of variance and have the eigenvalue higher than
Based on standard assumption of factorial analysis we hypothesize that our system of consumer profile should have no more than 5 variables. But considering the fact that all of actual series are in highly nonstable state the real set of independent variables is expected to be even lower. Using those qualitative arguments we propose to select 2 or 3 variables as indicators for consumer behavior in our system.
Table 6: Predictor Variables
Initial variable. Value Real/Proportion. Categorical  Representative variables. Real/ 
Proposed Variable. Real 

{Y}  Expenses for:  Common expenditure  
Y1  Alimentary goods  Basic expenditure  
Y2  Clothes  
Y3  Subsistence  
Y4  Alcoholic drinks and cigarettes  Extra expenditures  
Y5  Health*  
Y6  Transport  
Y7  Communication  
Y8  Culture and safety expenses  Qualitative Life Expenditure  Quality life and luxury expenditures 
Y9  Education  
Y10  Other services  
Y12  Family expenses  
Y13  Luxury goods  Luxury Expenditure  
Y14  Restaurant expenses 
We conclude that in our system, the most significant expenses contributing in the behavior of the consumers are normalized expenditures in “basic commodities and services”, in “some custom goods and services”, expenditures in “goods and services related to the quality of life” and “luxury expenses”. In this insight more detailed expenses consist in over detailed behavior and hence not matching good models. By estimation of most characteristics set of indicator variables we went more inside the relationship between factors and indicators. In this case we reconsider the variables as the exhibition of consumer behavior not only as result of direct measurement of particular activity. This last has as final result the decision that in substance consist in an agreement for what to do if two or more alternatives exist. The numerical value or even the rapport of any expenses to the total budget does not report a clear decision or clearly a decision of the consumer.
Our analysis is extended in a broader representation of consumer activity and his decision. The rapport between each category tells us which decision has been frontrunner after a reasonable rivalry between them. In this stage we avoid even behavioral classes and models because we are interested in final decision and cause that affect it, but surely one can discuss about them when interpreting results.
Logistic regression is a standardized model in this case as routinely recommended and used [
and the regression of the right hand side of (
In relation (
All characteristics above are attributes of the most frequently used to manage the expenses as stated in the survey.The statistics for each parameter has pvalue above 0.85 an only two have value above 0.95, but based on the arguments provided we accept this regression and acknowledge the description (
Using analysis of stationary for observed variables data as extra statistical tools has improved the study of specific econometric systems in the preliminary stage of model calculation end regression. It helped in filtering high disturbed data series that seem to not be drawn from a known distribution and hence they state is undefined. Next, knowing the level of stationary for actual state that characterized the variable we were able to judge on the expected range of significance in model fitting at least qualitatively, and motivate the model fitting in somewhat lower level of confidence but remaining valid. In the application to our concrete system in the limitation of small size sampler, we realized the study and obtained some characteristics. We obtained that the profile of the consumer was described by the binary variable that evaluates the dominance of basic needs expenses. The variables that define the predictors set are the size of the family, the nature of employment, education, the age group of householder and the budget. We observe that the category that weights mostly in the decision to spend in basic needs goods is the education level (highest score for highest level) , the second is the employment type, third is the age group etc. The budget has fine tune coefficient but its effect is important in the decision of the consumer. We expect that some of those finding can be extended to a larger system size and the methodology could be effective elsewhere.