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Math Help - Test for 3 independent variables, 1 dependent variable

  1. #1
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    Test for 3 independent variables, 1 dependent variable

    While I can sacrifice the complexity by testing the relation between the independent and dependent variables, I wonder whether there is any appropriate test to make a better use of the information collected:

    Independent categorical variable: alpha beta gamma
    Independent categorical variable: A B C D E
    Independent ordinal variable: 10 25 50 75 90
    Dependent continuous variable: (e.g.) -3.81, 0, 1.86, 0.59, -1.73 etc

    ANOVA repeated measures etc seems near but not. Any hints for my further study would be highly appreciated.
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  2. #2
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    Re: Test for 3 independent variables, 1 dependent variable

    Hey jas4710.

    Have you tried using an appropriate regression model or testing correlation between the variables?

    You should be able to setup an analyses that estimates the covariance matrix between the different random variables given the sample observations: have you tried this?
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  3. #3
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    Re: Test for 3 independent variables, 1 dependent variable

    Quote Originally Posted by chiro View Post
    Hey jas4710.

    Have you tried using an appropriate regression model or testing correlation between the variables?

    You should be able to setup an analyses that estimates the covariance matrix between the different random variables given the sample observations: have you tried this?
    Thanks chiro! After studying what "covariance matrix" can tell - "several properties or conditions or states being measured at the same time and that wed like to know if there is any relationship between those values", now let me go back to a simple question:

    Should I make a simple problem complicated?

    The first independent categorical variable alpha-beta-gamma is actually 3 hospitals located in near neighborhood;
    The second independent categorical variable A to E is actually 5 experienced doctors;
    The third independent ordinal variable 10 to 90 is actually 5 possible dosage administered;
    The Dependent continuous variable is actually a subjective score determined by that particular doctor (e.g. doctor C).

    So actually these 5 doctors are rotating around different hospitals and prescribe drugs at pre-determined dosage for patients and then give a health score for that patient. Assuming there is no experience gained from each prescription and I don't actually expect any correlation between these variables except from prescription dosage level, i.e. does higher dosage lead to higher score?

    In this sense, should I simply treat the 3 hospitals as repeated measure for a particular dosage? However, each doctor may have his own style in giving score. So again should I assess the doctor's scoring independently or together?

    Thank you again for your advice for helping better a healthcare system that shall ultimately benefit our society.
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  4. #4
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    Re: Test for 3 independent variables, 1 dependent variable

    If you want to actually estimate the correlation, then you should really consider estimating the co-variance matrix of your system given a random sample.

    Normalizing the co-variance matrix will give you a correlation matrix and you can then run a hypothesis test to see whether the true population correlation entry in the matrix is zero.

    If you have enough evidence to say that it is zero, then you can say you have enough evidence that it is correlated.

    If you want to test independence, then this is equivalent for showing P(A|B) = P(A) for any event or random variable B.

    I would suggest that if you are looking for any kind of relationship, that you should first perform a scatterplot for your variables to see if there is any kind of relationship (even if its non-linear) and then proceed to estimate the co-variance and then the correlation matrix.

    Then do a hypothesis test on a particular correlation value to see if there is evidence that the variables are correlated (In other words H0: p(i,j) = 0).

    Then based on this you can go further.

    Also if the results are correlated for each doctor in time, then you will need to use a longitudinal analysis which is more complicated.

    Finally, never make a simple problem complicated: it will always end up badly in the long run. If it is simple: keep it that way unless you absolutely have to add more complexity or assumptions to get a more realistic answer.
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