In hypothesis testing we use linear parameters. I am trying to work on factoring irrationality by using non linear modeling. I would like to factor the effect of correlation of the cause variable in the result.
Is this possible ? Is there any papers on this ?
Dear Raveendran,
There are no easy answers to the question in the way that you pose it. If you are trying to fit existing data in which you think that irrationality has created non-linear effects, then there are many methods available. Simple non-linearities can be captured in "linear" regression. You have only to introduce terms that correspond to the non-linearity of interest. For example, the chance of failure may be inversely correlated to capitol on hand, but it may also be correlated to the third power of the difference between capitol and and some threshold.
More generally you can replace linear regression with general additive models to greatly extend their range when some of your relationships are non-linear. Non-linear regression methods generally relate to a question of fitting method. You need to think carefully about how best to evaluate whatever model you decide to construct.
Good luck.
If you mean how can you model the "irrationality" (in quotes for reasons that are clear in the linked paper) then it is worth describing this irrationality. A good review is in:
http://library.mpib-berlin.mpg.de/ft/gg/GG_Homo_2009.pdf
The key thrust of the argument is that humans use procedures that appear non-optimal from some rational decision making perspectives, but are actually well-adapted for the situations in which the decisions are made (not always, but sometimes). If you mean just relaxing a model, follow Bruce's advice.
In decision theory (at least in multiple criteria decision making) there is what one calls "inconsistency" in judgements. Maybe you might consider these inconsistencies as one measure of irrationality. if you say you prefer a to b and you prefer b to c, and if you make another judgement saying you prefer c to a, you are being inconsistent. This is just a very simple example, the mathematics that capture inconsistent value judgements (and so eventually irrationality) are implemented in the software MACBETH, which is the state of the art software for this purpose. The following link leads you to a paper on the mathematics foundations of Macbeth: http://eprints.lse.ac.uk/22759/1/03061.pdf
If I had a regression sort of a model, I'd think about what rationality implies for my coefficients. As an example, if I were to estimate a perfectly competitive market, I'd expect to get that an increase in costs for everyone (such as, price of gas going up) by 1 penny per unit produced would translate to an increase in prices by 1 penny, and an increase by 2 pennies or half penny could be interpreted as irrationality. Now, there are other explanations too, like imperfect competition, etc, so estimating this stuff in the real world is harder, but the logic remains. Can you impose any restrictions on your coefficients that, if rejected, would imply irrationality?
Not being an expert on this problem, could we use a Monte Carlo approach in the final terms (or intermediate steps) to make decisions? It's being used in computational physics but you know...
https://en.wikipedia.org/wiki/Monte_Carlo_method
From the theoretical point of view, I agree with Daniel that you have to clearly define what you mean by "rationality"/"irrationality". Decision theory offers many extensions to the usual definition of rationality.
From the econometric point of view, there is a huge difference between non-linearity in parameters (which leads to models more difficult to estimate) and non-linearity in explanatory variables, which can be easily solved as suggested by Bruce.
The link between decision theory and econometrics has been studied in a series of papers published in Marketing Letters, following the choice symposium series:
https://www.researchgate.net/publication/268073893_Beware_of_black_swans_Taking_stock_of_the_descriptionexperience_gap_in_decision_under_uncertainty
https://www.researchgate.net/publication/230663764_Process_and_context_in_choice_models
https://www.researchgate.net/publication/5013280_Risk_Uncertainty_and_Discrete_Choice_Models
These 3 references question rationality and proposes methods to estimate the corresponding models.
Article Beware of black swans: Taking stock of the description–exper...
Article Process and Context in Choice Models
Article Risk, Uncertainty and Discrete Choice Models
Rationality is a very involved concept in decision theory. The only possible theoretical definition is that somedy who does not follow expected value of actions is not rational. The problem : what are the "good" probablities, in most situations nobody can answer. "The definition of rationality as coherence is impossibly restrictive; it demands adherence to rules of logic that a finite mind is not able to implement. Reasonable people cannot be rational by that definition, but they should not be brand as irrational for that reason". Kahneman 2009.
As Simon pointed out is rational who, depending on the time available and the energy he/she can or will devote to the problem, use his/her prefrontal cortex to build scenarios with reasonable subjective probabilities and make correct calculation avoiding the main cognitive biais.
see Pomerol, "Decison and Action", ISTE-Wiley for further developments about rationality and also the references to the comparison of expertise and linear regression in Kahneman 2011 chapter 20-21
Pomerol
I agree with Alexander J. Babchin that a general solution does not exist. However, that does not mean that we can't carve out specific cases and shed some light on them. If we must know many unknowable facts to be able to make totally rational decisions,we still may be able to to make a decisions based on probability. In a stochastic situation, perhaps we could define rationality as selecting one or more alternatives that have the highest probability of success. The decision will not always be right but will be most of the time.
Yes Marion but what are the probabilites, for example that the gallon of oïl be more than 70 $ within two years ?
Probabilities for predicting markets are difficult for an ordinary individual to know. Too many variables influence markets, including manipulation.
In decision making, rationality is subjective to a certain extent. If we have a set of decision criteria, a decision within that framework may appear to others as irrational if they are operating with different criteria. Examples can come from risk/reward scenarios.
Consider the following problem. Two drugs are used to treat intense pain. One drug has a high probability of providing a moderate decrease in pain, which still leaves some residual pain that interferes with normal abilities. No one dies from using it. A second drug provides a dramatic reduction in pain to almost normal (zero) levels but proves fatal to 1% of the population that uses it. Which drug choice constitutes the rational decision? It depends on your decision criteria. Whereas it is true that one cannot predict exact individual outcome from analyzing data obtained in past studies, one can use published probabilities if they exist. Suppose you want to maximize the probability of living and are willing to live in a debilitated state. If this is the most important decision criterion, select drug A. If, however, you would not like to live in such a condition and would rather try for a better life, and this is the most important criterion, select drug B. Each of the decisions appears to be irrational when applying the opposite criterion. However, the decisions are rational given the criteria used.
To consider another example, what constitutes a rational decision can depend on habits and experience. A decision about what to do in an emergency situation may seem rational to a novice who may be more likely to be influenced by emotions. However, to a person with more expertise, the same decision may appear to be irrational because the expert has more knowledge and experience and is aware of more options.
Hope this helps.