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Math Help - hypothesis testing comparing 2 multiple regression models

  1. #1
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    Angry hypothesis testing comparing 2 multiple regression models

    Hi guys, I beg u to help me with this:

    Currently I have 2 models
    y1 = a1*x1 + b1*z1 + c1
    y2 = a2*x2 + b2*z2 + c2

    y1 is taken from 18 data samples.
    y2 is taken from 72 data samples.

    I want to perform null hypthesis as a1 = a2, b1=b2, c1=c2.
    My goal is to show that first model is different than second model.

    Do u know some links or books that can be useful to me?
    or maybe u can help me to figure out what I should do.....
    Thanks so much.... I'm so desperate with this...


    //////////////////////////////////////////////////////////////


    I couldn't find any relevant examples for this problem
    Usually... the example is only
    y1 = a1*x1 + c1
    y2 = a2*x2 + c2
    with null hypothesis, a1 = a2, c1 = c2.

    And it's not sufficient for my case....

    or the other pupolar example is
    y = a*x1 + b*x2 + c*x3 + d*x4
    with null hypothesis, a = b.

    And it's not sufficient for my case....

    //////////////////////////////////////////////////////////////


    I used R statistical package to provide the model.
    But after that I'm lost.....

    Thanks for your big help
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  2. #2
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    Quote Originally Posted by neosonic View Post
    Hi guys, I beg u to help me with this:

    Currently I have 2 models
    y1 = a1*x1 + b1*z1 + c1
    y2 = a2*x2 + b2*z2 + c2

    y1 is taken from 18 data samples.
    y2 is taken from 72 data samples.

    I want to perform null hypthesis as a1 = a2, b1=b2, c1=c2.
    My goal is to show that first model is different than second model.

    Do u know some links or books that can be useful to me?
    or maybe u can help me to figure out what I should do.....
    Thanks so much.... I'm so desperate with this...


    //////////////////////////////////////////////////////////////


    I couldn't find any relevant examples for this problem
    Usually... the example is only
    y1 = a1*x1 + c1
    y2 = a2*x2 + c2
    with null hypothesis, a1 = a2, c1 = c2.

    And it's not sufficient for my case....

    or the other pupolar example is
    y = a*x1 + b*x2 + c*x3 + d*x4
    with null hypothesis, a = b.

    And it's not sufficient for my case....

    //////////////////////////////////////////////////////////////


    I used R statistical package to provide the model.
    But after that I'm lost.....

    Thanks for your big help
    When faced with a stats problem that I don't know much about
    I usually consider using some form of Monte-Carlo method to
    investigate the distribution of the parameters of interest.

    For instance your models are in reality of the form:

    y=ax+by+c+r

    where r is a noise term usually (if things are going right) zero mean
    normal with sd s say, which you can estimate from the residuals.
    (note if the residuals show noticeable departures from independence and
    normality you are in trouble and need to reconsider the models)

    Now assume some value of a, b and c (the same for both samples) and
    generate 100 (or a 1000 or whatever) replicates of the estimates of
    (a1-a2, b1-b2, c1-c2), and compute an estimate of the covariance matrix
    of this vector for the 100 replicates.

    The vector (a1-a2, b1-b2, c1-c2) that you observe should be more
    or less multivariate normal, and we now have an estimate of its
    covariance matrix, so we can test it (you will have to look up test for
    the this).

    This sort of analysis is of an exploratory nature and will give a rough
    indication if the models are significantly different.

    For a more theoretical (academically respectable) approach you will need to
    look at a reference on regression models, or general linear models (GLM).
    There should be a vast literature on testing such models, which I am not
    familiar with.

    RonL
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  3. #3
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    Quote Originally Posted by neosonic View Post
    Hi guys, I beg u to help me with this:

    Currently I have 2 models
    y1 = a1*x1 + b1*z1 + c1
    y2 = a2*x2 + b2*z2 + c2

    y1 is taken from 18 data samples.
    y2 is taken from 72 data samples.

    I want to perform null hypthesis as a1 = a2, b1=b2, c1=c2.
    My goal is to show that first model is different than second model.

    Do u know some links or books that can be useful to me?
    or maybe u can help me to figure out what I should do.....
    Thanks so much.... I'm so desperate with this...


    //////////////////////////////////////////////////////////////


    I couldn't find any relevant examples for this problem
    Usually... the example is only
    y1 = a1*x1 + c1
    y2 = a2*x2 + c2
    with null hypothesis, a1 = a2, c1 = c2.

    And it's not sufficient for my case....

    or the other pupolar example is
    y = a*x1 + b*x2 + c*x3 + d*x4
    with null hypothesis, a = b.

    And it's not sufficient for my case....

    //////////////////////////////////////////////////////////////


    I used R statistical package to provide the model.
    But after that I'm lost.....

    Thanks for your big help
    The test you're looking for is a Chow Test. The test statistic is


    where RSS1 is the sum of squared residuals from the first regression, RSS2 is from the second regression and RSS is from the pooled regression.
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  4. #4
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    Oct 2006
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    Smile Thanks, by the way, how do we get RSS?

    Quote Originally Posted by JakeD View Post
    The test you're looking for is a Chow Test. The test statistic is


    where RSS1 is the sum of squared residuals from the first regression, RSS2 is from the second regression and RSS is from the pooled regression.
    Wow, thanks guys... I appreciated much...
    This is my 100% project testing... thx so much.

    Yup, chow test is very acceptable in this case
    By the way... how do we get RSS?
    is RSS = RSS1 + RSS2 in this case?

    Thanks Bro, God bless
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  5. #5
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    Quote Originally Posted by neosonic View Post
    By the way... how do we get RSS?
    It's from the pooled regression, which has all the observations in it.
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  6. #6
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    Thumbs up Thanks Bro:)

    Thanks Bro, it's the final step of my calculation
    Just need to confirm, k in this case is 3 rite? (k in chow test formula applied to my model).

    Thanks, God bless
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  7. #7
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    Quote Originally Posted by neosonic View Post
    Just need to confirm, k in this case is 3 rite? (k in chow test formula applied to my model).

    Thanks, God bless
    Yes and you're welcome!
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