+ Reply to Thread
Page 1 of 6 1 2 3 4 5 6 LastLast
Results 1 to 15 of 76

Thread: Multivariate linear regression analysis (multiple dependent variable, one independent

  1. #1
    Points: 1,083, Level: 17
    Level completed: 83%, Points required for next Level: 17

    Posts
    36
    Thanks
    33
    Thanked 0 Times in 0 Posts

    Multivariate linear regression analysis (multiple dependent variable, one independent




    I am trying to determine the reason why(and how many) people with health insurance do not fully use all of its benefits(like free flu vaccines). I am using a sample of 400 people with age, income, education as dependent variables and having health insurance as independent variable. I glanced at the information in http://www-01.ibm.com/support/docvie...id=swg21476743 and followed the mentioned steps.

    I got some results like

    Multivariate Tests (Design: Intercept + haveinsure)

    Effect Value F Hypothesis df Error df Sig.

    Intercept Pillai's Trace .053 11.361(b) 3.000 470.000 .000

    Wilks' Lambda .827 11.361(b) 3.000 470.000 .000

    Hotelling's
    Trace .069 11.361(b) 3.000 470.000 .000

    Roy's Largest
    Root .083 11.361(b) 3.000 470.000 .000


    haveinsure Pillai's Trace .138 4.570 12.000 1420.000 .000

    Wilks' Lambda .877 4.797 12.000 1248.086 .000

    Hotelling's
    Trace .151 4.998 12.000 1410.000 .000

    Roy's Largest
    Root .141 16.101(c) 4.000 473.000 .000

    b - Exact statistic
    c The statistic is an upper bound on F that yields a lower bound on the significance level







    Tests of Between-Subjects Effects Tests

    Source Dependent
    Variable Type III df Mean F Sig.
    Sum of Squares Square

    Corrected Model age 37.546(a) 4 9.637 3.893 .004
    education 10.619(b) 4 2.655 .477 .752
    income 334.245(c) 4 84.061 16.766 .000

    Intercept age 32.173 1 34.173 13.805 .000
    education 141.268 1 143.268 25.752 .000
    income 30.201 1 30.201 6.024 .014

    haveinsure age 37.546 4 9.637 3.893 .004
    education 10.619 4 2.655 .477 .752
    income 335.245 4 84.061 16.766 .000

    Error age 1171.320 474 2.475
    education 2636.013 474 5.563
    income 2375.494 474 5.014

    Total age 3150.000 479
    education 12315.000 479
    income 6289.000 479

    Corrected Total age 1210.866 478

    education 2646.633 478

    income 2711.739 478


    a. R Squared = .032 (Adjusted R Squared = .024)
    b. R Squared = .004 (Adjusted R Squared = -.004)
    c. R Squared = .124 (Adjusted R Squared = .117)





    Dependent Parameter B Std. t Sig. 95% Confidence Interval
    Variable Error Lower Upper
    Bound Bound

    age Intercept 1 1.573 0.637 0.525 -2.092 4.092
    [haveinsure=1] 1.173 1.576 0.745 0.456 -1.923 4.268
    [haveinsure=2] 0.589 1.578 0.373 0.708 -2.514 3.693

    education Intercept 4 2.358 1.697 0.091 -0.635 8.636
    [haveinsure=1] 0.578 2.362 0.245 0.808 -4.063 5.219
    [haveinsure=2] 0.388 2.367 0.164 0.87 -4.265 5.04

    income Intercept 1 2.238 0.448 0.659 -3.4 5.4
    [haveinsure=1] 2.289 2.242 1.021 0.309 -2.118 6.696
    [haveinsure=2] 0.419 2.245 0.188 0.852 -3.999 4.837

    1. Am I approaching the problem in a proper way? I mean am I doing the right analysis in SPSS?

    2. Which method(Pillai's Trace, Wilks' Lambda, Hotelling's Trace, Roy's Largest Root) should be used for a case like mine?

    3. Why is Type III Sum of Squares error 1171.320 for age, education and income?

    4. I am new to Multivariate linear regression analysis. How can I interpret and learn more about the output SPSS generated?

    Any suggestions would be appreciated.

    Thanks

  2. #2
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Quote Originally Posted by p_s View Post
    I am trying to determine the reason why(and how many) people with health insurance do not fully use all of its benefits(like free flu vaccines).
    The most usual thing in this situation would be to think of "insurance" variable as a dependent variable and "age", "income" and "education" as explanatory variables, that is as independent variables. Then you would have a model as something like this one:

    insurance = a +b1*age + b2*income +b3* education + error

    That would be called a multiple regression model. (Skip the thoughts about multivariate models. That is an other thing.)

    But if the insurance variable is a "have" or "do not have" insurance, the you will need to use a logistic = logit model:

    log(p/(1-p)) = a +b1*age + b2*income +b3* education

    Where p is the proportion having an insurance at the given value of the explanatory variables. Don't worry if it looks complicated. The computer takes care of it and estimates the b1, b2 and b3 and gives you significance test.

  3. The Following User Says Thank You to GretaGarbo For This Useful Post:

    p_s (08-04-2014)

  4. #3
    Points: 1,083, Level: 17
    Level completed: 83%, Points required for next Level: 17

    Posts
    36
    Thanks
    33
    Thanked 0 Times in 0 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Thanks GretaGarbo:

    Quote Originally Posted by GretaGarbo View Post
    The most usual thing in this situation would be to think of "insurance" variable as a dependent variable and "age", "income" and "education" as explanatory variables, that is as independent variables. Then you would have a model as something like this one:

    insurance = a +b1*age + b2*income +b3* education + error

    That would be called a multiple regression model. (Skip the thoughts about multivariate models. That is an other thing.)
    I think insurance can be a dependent variable if I was trying to study how age, income and education influence if a person has insurance or not.

    However, I am trying to determine the reason why(and how many) people with health insurance do not fully use all of its benefits(like free flu vaccines).
    Quote Originally Posted by GretaGarbo View Post
    But if the insurance variable is a "have" or "do not have" insurance, the you will need to use a logistic = logit model:

    log(p/(1-p)) = a +b1*age + b2*income +b3* education

    Where p is the proportion having an insurance at the given value of the explanatory variables. Don't worry if it looks complicated. The computer takes care of it and estimates the b1, b2 and b3 and gives you significance test.
    Well, in a sample of 400 people, say 300 folks have insurance, so I am taking these 300 people and want to know which of these 300 do not use the free services like flu vaccines, routine health checkups and why? Is it because those folks are too young(is age a factor) to know benefits of flu vaccines, routine health checkups or these people do not know enough(lack of education) about the benefits or something else?

    Which model should I use?

    I appreciate your assistance and time.

  5. #4
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Then, the dependent variable is "use" or "use not" the insurance. That will be the dependent variable and "age", "income" and "education" are explanatory variables.

    The sample size is 300, those who are insured. You can not know anything about those who are not insured, so they are not a part of the population you are interested of. So skip the 100 who are not insured.

  6. The Following User Says Thank You to GretaGarbo For This Useful Post:

    p_s (08-08-2014)

  7. #5
    Points: 1,083, Level: 17
    Level completed: 83%, Points required for next Level: 17

    Posts
    36
    Thanks
    33
    Thanked 0 Times in 0 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Thanks GretaGarbo:

    Quote Originally Posted by GretaGarbo View Post
    Then, the dependent variable is "use" or "use not" the insurance. That will be the dependent variable and "age", "income" and "education" are explanatory variables.

    The sample size is 300, those who are insured. You can not know anything about those who are not insured, so they are not a part of the population you are interested of. So skip the 100 who are not insured.
    So, should I use logistic regression http://www.ats.ucla.edu/stat/spss/dae/logit.htm and binary logistic in SPSS(Analyze->Regression->Binary Logistic regression) since the dependent is dichotomous(people use preventive care services or not)?

    I tried understanding the output of how SPSS does it http://www.ats.ucla.edu/stat/spss/output/logistic.htm and I need to know more to interpret it correctly.

    I appreciate your assistance and time.

  8. #6
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Quote Originally Posted by p_s View Post
    So, should I use logistic regression
    Yes, use logit.

  9. The Following User Says Thank You to GretaGarbo For This Useful Post:

    p_s (08-08-2014)

  10. #7
    Points: 1,083, Level: 17
    Level completed: 83%, Points required for next Level: 17

    Posts
    36
    Thanks
    33
    Thanked 0 Times in 0 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Thanks GretaGarbo,
    Quote Originally Posted by GretaGarbo View Post
    Yes, use logit.
    1. In SPSS 22, can I chose Analyze->Regression->Binary Logistic, then chose utilize preventive services as dependent and age, income, education as covariates.

    2. For methods, there are few like forward conditional, forward LR, forward Wald. Which are used for cases like mine?

    3. Can selection variable be left blank?

    4. How can a layman like me get a primer on this and how to do it in SPSS?

    Thank you for your advice and time.

  11. #8
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Quote Originally Posted by p_s View Post

    1. In SPSS 22, can I chose Analyze->Regression->Binary Logistic, then chose utilize preventive services as dependent and age, income, education as covariates.)
    OK.
    (Maybe you want to make one of the variables to a "categorical" variable, if e.g. "education" has different categories.


    Quote Originally Posted by p_s View Post
    2. For methods, there are few like forward conditional, forward LR, forward Wald. Which are used for cases like mine?
    Just use the "Enter" method. The rest of them are crazy stepwise regression methods (the "forward" and "backwards" stuff.) Don't use that! Formulate you model. Estimate it. Think about the result and write down your thoughts about the results. Then possibly, reformulate the model (include or delete model terms) and re-estimate and think again.


    Quote Originally Posted by p_s View Post
    3. Can selection variable be left blank?
    Yes.

    Quote Originally Posted by p_s View Post
    4. How can a layman like me get a primer on this and how to do it in SPSS?
    I am not sure of what the English word primer means, but of you ask someone here to write a private guide for you, the answer is no! Otherwise, search the internet! And look in your own textbooks about regression and analysis of variance.

  12. The Following User Says Thank You to GretaGarbo For This Useful Post:

    p_s (08-08-2014)

  13. #9
    Points: 1,083, Level: 17
    Level completed: 83%, Points required for next Level: 17

    Posts
    36
    Thanks
    33
    Thanked 0 Times in 0 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Thanks GretaGarbo,

    Quote Originally Posted by GretaGarbo View Post
    OK.
    (Maybe you want to make one of the variables to a "categorical" variable, if e.g. "education" has different categories.
    1. Yes, education has different categories, how can that be separated?

    2. Also, do I need to change contrast(default is Indicator) and reference category?

    Quote Originally Posted by GretaGarbo View Post
    Just use the "Enter" method. The rest of them are crazy stepwise regression methods (the "forward" and "backwards" stuff.) Don't use that! Formulate you model. Estimate it. Think about the result and write down your thoughts about the results. Then possibly, reformulate the model (include or delete model terms) and re-estimate and think again.
    I expect people having more education and income will be using more of preventive health services(like free flu vaccines). I also anticipate older folks will be using more free routine physical check ups. I know gender also matters so changing this variable might affect the results. Is this is the proper way to think about a model, estimate and re-estimate it with some factors removed?



    Quote Originally Posted by GretaGarbo View Post
    I am not sure of what the English word primer means, but of you ask someone here to write a private guide for you, the answer is no! Otherwise, search the internet! And look in your own textbooks about regression and analysis of variance.
    Sorry, I did not mean to be a freeloader. I realize all too well that public forums exist due to kind and knowledgeable volunteers like you. I was asking if there are some good web links which a layman like me can study to tackle the problem at hand. As you can notice, my background is not in statistics, but for this task I have to know this. Just as there are beginner level tutorials for calculus which explain the minimum, someone attempting to solve calculus must know, I thought there might be some web tutorials for logistic regression which someone can point me to. Searching led me to http://bama.ua.edu/~jhartman/689/mlr.ppt and http://www.nemoursresearch.org/open/...011/Class6.ppt which explain steps in linear regression in SPSS
    and https://onlinecourses.science.psu.edu/stat501/node/86
    Thank you again for your time and advice.
    Last edited by p_s; 08-07-2014 at 10:13 PM.

  14. #10
    Points: 132, Level: 2
    Level completed: 64%, Points required for next Level: 18
    Phaedrus's Avatar
    Posts
    15
    Thanks
    3
    Thanked 1 Time in 1 Post

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    UCLA has lots of "guides" for SPSS, Stata, and R. For instance: http://www.ats.ucla.edu/stat/spss/

  15. The Following User Says Thank You to Phaedrus For This Useful Post:

    p_s (08-08-2014)

  16. #11
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Quote Originally Posted by p_s View Post
    1. Yes, education has different categories, how can that be separated?
    Just declare it as a category variable in the category box.

    Quote Originally Posted by p_s View Post
    2. Also, do I need to change contrast(default is Indicator) and reference category?
    No, you don't need to do that.


    If you are not sure about the meaning or interpretation of the estimates, then you can make up some data (a very small data set) with with very clear pattern. For example with only a clear difference between gender. Experiment with such small fake data sets so that you understand the meaning of the parameter estimates.

  17. The Following User Says Thank You to GretaGarbo For This Useful Post:

    p_s (08-08-2014)

  18. #12
    Fortran must die
    Points: 58,790, Level: 100
    Level completed: 0%, Points required for next Level: 0
    noetsi's Avatar
    Posts
    6,532
    Thanks
    692
    Thanked 915 Times in 874 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    As others have noted you can not have more than one dependent variable in regression (there are other methods like MANOVA and SEM that do this but not multivariate regression where the multi refers to the predictors not the predicted variable). If you want to know why a predictor is behaving as it is, as you suggested, you might model this separately. That is model what is causing variation in insurance as a separate analysis (there is a specialized form of regression called multilevel regression which supports this, but if you are new to regression that is a big step up in complexity).

    If you use logistic regression remember to request the Odds Ratios. These are far more useful to interpret than the slopes in terms of the impact of the predictor (the slopes are difficult to interpret in term of the original predicted variable except for the sign and statistical signficance).
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

  19. The Following User Says Thank You to noetsi For This Useful Post:

    p_s (08-08-2014)

  20. #13
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Quote Originally Posted by noetsi View Post
    multivariate regression where the multi refers to the predictors not the predicted variable
    Well, I don't know what Noetsi mean by "multivariate" or "predictors" or "predicted variable".

    But in my book multivariate regression is a situation where there are several dependent variables, like in the output in the first post, and one or several explanatory variables. And multiple regression is where there are several explanatory variables (also called independent variables) like "age", "income" and "education".

    Thus, I suggest to use a logistic multiple regression with "use" or "not use" of insurance as dependent variable, and "age", "income" and "education" as explanatory variables.


    Quote Originally Posted by noetsi View Post
    If you want to know why a predictor is behaving as it is, as you suggested, you might model this separately.
    As I understand it, there is a general agreement that it it advantageous to include all relevant explanatory variables in a multiple regression model. (Among other things to avoid "omitted-variable-bias".) And that it is not so good to do separate regressions for each explanatory variable and try to conclude something about the influence of each variable.

    Quote Originally Posted by noetsi View Post
    If you use logistic regression remember to request the Odds Ratios. These are far more useful to interpret than the slopes in terms of the impact of the predictor
    I agree about this one.

  21. #14
    Fortran must die
    Points: 58,790, Level: 100
    Level completed: 0%, Points required for next Level: 0
    noetsi's Avatar
    Posts
    6,532
    Thanks
    692
    Thanked 915 Times in 874 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen

    Multivariate regression is referenced in the title and commonly in the literature. As I explained this term refers not to the variable you are predicting [which is given various titles in the literature including response and dependent variable] but what you are predicting it with [called independent variables often although there are many terms used in the literature]. Because there are so many terms used for the same thing, I stuck with functional ones, showing what is being predicted [the Y on the left side of the equation] and what you are using to predict it with [the X on the right side of the equation].

    I thought the author was, in additing to explaining the original dependent variable, also trying to explain one of the predicting [or independent] variables and suggested an approach to do so. But I misread what they said originally.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

  22. The Following User Says Thank You to noetsi For This Useful Post:

    p_s (08-08-2014)

  23. #15
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: Multivariate linear regression analysis (multiple dependent variable, one indepen


    Frankly, I don't understand what Noetsi is saying and what he mean by "multivariate regression".

    For those interested here is a link to one text and here is a common used textbook (page 388).

  24. The Following User Says Thank You to GretaGarbo For This Useful Post:

    JesperHP (08-14-2014)

+ Reply to Thread
Page 1 of 6 1 2 3 4 5 6 LastLast

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats