Heteroskedasticity

HETEROSKEDASTICITY:

Is your JOY heteroskedastic? or homoskedastic?

*The homoskedasticity assumption states that “the variance of the unobservable error, u, conditional on the explanatory variables, is constant.”

Var (u | x1 , … , xk) = σ2

In the equation

wage = β0 + β1 educ + β2 exper + β3 tenure + u ,

homoskedasticity requires that the variance of the unobserved error u does not depend on the levels of education, experience, or tenure.

Homoskedasticity fails whenever the variance of the unobservables changes across different segments of the population, where the segments are determined by the different values of the explanatory variables.

For example, in a savings equation, heteroskedasticity is present if the variance of the unobserved factors affecting savings is not constant, e.g., increases with income.

Is your JOY heteroskedastic? or homoskedastic?

Joy equation

In the JOY equation above, our Model predicts that your level of Cheerfulness is a function of: wealth (the amount of money you have in your pocket), grace (which presumably is a function of how much you pray and your closeness to Jesus Christ and His mercy towards you), ambience (a.k.a. the environment or your surroundings), and struggle (the amount of fight [lucha], interior and exterior, you put in.  [What do you think are the magnitude and direction (+ or ) of β1, β2, β3, and β4?]

The error term, u, is supposed to capture all the other factors that explain ‘Joy’ that we may have failed to account for in our Model.  We can never really tell what we may have missed out on, unless we go on a Sherlock Holmes trek toward capturing what those true factors are in the population….

Let’s just hypothesize, for now, that one such factor is “doing an insanity-causing PhD [coursework or DISSERTATION]”.  Let’s set aside for the moment what the beta-coefficient of such a variable would be (although I surmise it’s a resounding NEGATIVE…).  Heteroskedasticity would be present if the variance in such an unobserved factor were to be non-constant, that is, it does not remain the same, i.e., σ2.

In layman’s terms: the “insanity-causing PhD” makes my life go haywire, and my relationship with it goes on a rollercoaster ride! 😦  ¿Entiendes? So, I therefore conclude … that my JOY is … heteroskedastic!!! Boo-hoo! T.T

Cosa facciamo? ¿Qué hacer? Hmm, I know! I’ve found another ‘hidden explanatory factor’ for our ‘Joy equation’ above: MUSIC!!! Let’s sing! ¡Vamos a cantar! Do you know the song “I Will Sing Forever”?  Here goes:

http://www.storage.to/get/2iC5q37Q/I_Will_Sing_Forever___Full.MID

(If you have Finale Notepad, & you can’t find the score on the Internet, I can send you the Music Sheet (.mus file). Drop me an email…)

I WILL SING FOREVER OF YOUR LOVE, O LORD:

I will sing forever of Your love, O Lord;

I will celebrate the wonder of Your name;

For the word that You speak

is a song of forgiveness

and a song of gentle mercy and of peace.

Let us wake at the morning and be filled with Your love

and sing songs of praise all our days,

For Your love is as high as the heavens above us

and Your faithfulness as certain as the dawn.

I will sing forever of Your love, O Lord;

for You are my refuge and my strength

You fill the world with Your life-giving Spirit

that speaks Your word,

Your word of mercy and of peace.

And I will sing forever of Your love, O Lord

Yes, I will sing forever of Your love, O Lord!

🙂  🙂  🙂

I saw this just now, on “PhD Comics” group in FB,

in answer to the Forum question “You know you’re a PhD student when…”

“…you realize that you must use non-parametric test because the Ph.D life is not normally distributed”.  Hahaha!

PhD-comic-4

http://www.phdcomics.com/

PhD-comic-3

🙂  🙂  🙂

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6 Responses to “Heteroskedasticity”

  1. Richy N Meggy Says:

    transformation ms aliza kung ayaw parin ma-meet ang assumption na yan, do nonparametric test.

  2. alizaracelis Says:

    Thanks, Wilf! My problem is, my sample size is not so big, so I’m afraid I lose degrees of freedom [also in the spiritual sense 😉 ]. But will mention it to Chipi… Um, ‘BLUE’ results? Um, I only know MAROON results 😉 😀 😀 😀 😛 (notice the color of this blog?!?) Ok, will pray for your abstract submission! Hey, Lisbon, nice! Can I go with you? 🙂

  3. Wilf Says:

    Hi Aliza:

    If you have problems with serial correlation (see Chipi’s comment) try using the generalized method of moments using the Newey-West covariance estimator, which allows you to drop the assumptions of normality and homoscedasticity, to get BLUE results even in the presence of autocorrelation. I hope I still remember my econometrics. I am due to submit a research abstract tomorrow for a conference in Lisbon in July 2010.

  4. alizaracelis Says:

    Gosh, Chipi, your comments are really…great! as in, [statistically] SIGNIFICANT! THANKS!!! Hmm, with your useful ideas, I think I can move on with my statistical analyses and results… 🙂 …’Without counting the costs’, you say… but, um, I’m a COST accountant, you see? 😦 Oh, well, I’d better hibernate & concentrate… Luckily, I’ve managed to stay out of Mafia Wars on FB! 😉 😀 Say HELLO to Tina for me! :X

  5. Chipi Buenafe Says:

    Well, before even discussing whether joy is heteroskedastic or homoskedastic, it might be good to check whether the model itself is correctly specified or not. Hehe!

    With the exception of wealth, all of the other variables in the model will need to have a good reliable proxy for the estimation to work. You even have more problems of getting good data for the hard variables, like grace (how can one actually measure this??!?!?).

    Also, you may need to consider time series stuff here. Is joy contemporaneous to struggle? Or will it necessary have lagged effects? And then you get the problem of whether the model above suffers from serial correlation or not.

    Bottomline, all of our problems concerning these things focus on the property of the error terms. Given that life is generally out of our complete control most of the time, you might as well use a different estimation technique, like maximum likelihood estimators or Monte Carlo generators. (Read: make the most out of life without counting [the costs or the independent/control variables].)


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