Chow test to compare regression on two groups
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Chow test to compare regression on two groups
 
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Hello!
I would like to ask if I should use the Chow test to check which variables are different between two groups regressions. The design has a VD (depression) and several VI's (coping styles), and I would like to know if coping styles that predict depression are different between women and men (group). Does it make sense to use Chow test? Thanks in advance! José |
Re: Chow test to compare regression on two groups
Administrator
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According to the Wikipedia page, at least (http://en.wikipedia.org/wiki/Chow_test), the Chow test is an omnibus test, with a null hypothesis which specifies that b0_male = b0_fem, b1_male = b1_fem, b2_male = b2_fem, etc. From your wording above, though, I suspect you want to examine each variable individually--i.e., you want to allow for the possibility that some variables interact with sex, while others don't. So why not just include the product terms, Sex*IV1, Sex*IV2, etc? E.g., suppose you have 3 X-variables plus Sex (coded 0/1). The model would be: Y' = b0 + b1*X1 + b2*X2 + b3*X3 + b4*Sex + b5*X1*Sex + b6*X2*Sex + b7*X3*Sex The null hypothesis for each of those product terms is that the effect of that IV (whatever the effect is) is the same for males and females. Or, looking at it the other way, the difference between males and females is the same for all values of that IV.
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Chow test to compare regression on two groups
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Thanks for your reply!
I have done this syntax: UNIANOVA depression BY sex WITH coping1 coping2 coping3 coping4 coping5 coping6 /METHOD=SSTYPE(3) /INTERCEPT=INCLUDE /CRITERIA=ALPHA(0.05) /DESIGN= coping1 coping2 coping3 coping4 coping5 coping6 sex*coping1 sex*coping2 sex*coping3 sex*coping4 sex*coping5 sex*coping6 The results showed that coping6 is significative. So can I state that coping6 is different between males/females predicting depression? José |
Re: Chow test to compare regression on two groups
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Administrator
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I don't see the main effect of sex on your /DESIGN line. You need it too. I.e., /DESIGN= sex coping1 coping2 coping3 coping4 coping5 coping6 sex*coping1 sex*coping2 sex*coping3 sex*coping4 sex*coping5 sex*coping6 I would also add a "/PRINT parameter" sub-command to get the table of regression coefficients.
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Chow test to compare regression on two groups
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In reply to this post by Jose Rocha
At 02:35 PM 9/14/2010, Jose Rocha wrote:
I have done this syntax: First, is it coping6 or sex*coping6 that's significant? If it's coping6, that shows nothing about difference between males and females. Second, testing all six sex*copingN interactions individually is an instance of multiple comparisons. That multiplies your chance of getting a significant result where there's no underlying effect ("Type I error"). Applying the Bonferroni correction, which is admittedly conservative, you should report the sex*coping6 as significant only if you have p<.05/6, i.e. p<.008. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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In reply to this post by Jose Rocha
Jose,
Are your coping style variables, binary variables (coded 0/1)? Is it possible for a subject to endorse more than one coping style? What exactly does your data set look like?
Does your data set look like this?:
subj sex coping1 coping2 coping3 coping4 coping5
1 1 0 1 0 0 0
2 2 1 0 0 0 0
3 2 0 1 0 0 0
.
.
.
Ryan
On Tue, Sep 14, 2010 at 2:35 PM, Jose Rocha <[hidden email]> wrote: Thanks for your reply! |
Re: Chow test to compare regression on two groups
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In reply to this post by Bruce Weaver
Bruce:
Yes, I tried to include "sex" but it changed the results, and none coping*sex was significative (.05). I am out of office, tomorrow I will past the table of regression. That suggestion is great! Richard: It was the sex*coping6 that was significant. I guess you gave the answer about the reason the inclusion of "sex" alone gets less significant values. How can I include bonferroni correction? R B: Considering the type of coping variables, they are not binomial, they are continuous. And each subject has values for all 6 coping styles. Those results came from a specific scale/sub-scale scores. Thanks again for your nice comments and suggestions. I will follow this discussion with the table of regression coefficients. José |
Re: Chow test to compare regression on two groups
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Administrator
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It would help if you reported the samples sizes (males & females) too, José. With this many parameters in the model, there could be danger of over-fitting. For a good discussion of this topic, see Mike Babyak's nice article. http://www.class.uidaho.edu/psy586/Course%20Readings/Babyak_04.pdf Cheers, Bruce
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Chow test to compare regression on two groups
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100 females, 19 males. I will read it. José |
Re: Chow test to compare regression on two groups
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In reply to this post by Richard Ristow
Richard's comment raises a point that I've thought about frequently. It seems to me that when it comes to linear models that contain both categorical and continuous explanatory variables, the world can be divided into two camps: 1. the ANOVA camp, and 2. the regression camp. The ANOVA camp tends to be made up of folks who do designed experiments (e.g., experimental psychologists. The regression camp tends to be made up of people who work with observational data. Personally, I started off in the ANOVA camp, as a psychology student; but after starting to work for people doing medical and health-related research, I've shifted somewhat (but not completely) toward the regression camp. I won't ramble on at great length, but here are a few of the differences that I've noticed between these camps. a) ANOVA folks who are doing designed experiments are content with MUCH smaller sample sizes than are regression folks. In some experimental fields, researchers would say that group sizes well below 10 are just dandy. For regression, the rules of thumb suggest that much larger samples would be needed (e.g., http://www.angelfire.com/wv/bwhomedir/notes/linreg_rule_of_thumb.txt). b) In the basic ANCOVA model, ANOVA folks are much more concerned than regression folks about equality of the groups on the covariate. In fact, some ANOVA campers argue that the ANCOVA model should only be used when there is random assignment to groups. But regression campers view ANCOVA as a regression model with one continuous and one explanatory variable, and are often unconcerned about whether or not there was random assignment to groups. c) ANOVA folks are much more concerned than regression folks about correcting for multiple tests. E.g., suppose you had a study with several treatments compared to a common control. ANOVA campers would likely use Dunnett's test to control the family-wise error. Regression campers, on the other hand, would create k-1 indicator variables for the treatments, and use the t-tests on those k-1 coefficients without any correction. I've always found this last example rather curious, given that running it as an ANOVA or a regression doesn't change anything--it's exactly the same model in both cases. I suppose it just goes to show how big a role convention plays in all of the various fields. Getting back to Richard's point, I do agree that regression campers ought to be more concerned about the multiple testing problem than they often are. Oh yes...one more difference just occurred to me. d) ANOVA campers love the interaction. Traditionally, regression campers have not been very fond of interactions, and have gone to great lengths to avoid having them in their models. I suspect this is because they struggle to interpret what the coefficients for the product terms mean, and they often fail to understand that the coefficients for main effects are really simple main effects, etc. Books like the one by Aiken & West can help a lot in this regard, though. Cheers, Bruce
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Chow test to compare regression on two groups
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Good points by Bruce Weaver. To comment on one of them, at 05:49 PM
9/14/2010, he wrote: >d) ANOVA campers love the interaction. Traditionally, regression >campers have not been very fond of interactions, and have gone to >great lengths to avoid having them in their models. I suspect this >is because they struggle to interpret what the coefficients for the >product terms mean, and they often fail to understand that the >coefficients for main effects are really simple main effects, etc. (I was, at least first, a regression camper.) Another reason regression-camp people stir shy of interactions is that they're (we're) oriented toward continuous independent variables. In a discrete-variable (classic ANOVA) model, the 'interaction' terms fully characterize the interaction between the factors. In a continuous-variable model, if X and Y are the independent variables, adding X*Y doesn't remotely exhaust the ways the two can interact. For that reason, I prefer calling X*Y a 'cross-term' rather than an 'interaction'. And since X*Y is a second-order term (if both values grow in the same proportion, it grows as the square of that proportion), including X*Y can be taken to require including X**2 and Y**2 as well; and suddenly, it's a much more complicated model. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Chow test to compare regression on two groups
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In reply to this post by Bruce Weaver
I feel more like an hybrid or camping on both sides. I have been researching on clinical and health psychology.
I guess the sample issue here is complex, since I have mixed strategies. Nevertheless, more is always better. I can restrict the number of predictive variables (IV's) based on some criteria, but if i include just one of those sex*copingN variables the result is always significative... (p=.000) José |
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In reply to this post by Richard Ristow
I either don't understand or don't agree with this statement. You say
that if there's an X*Y interaction term, then (either? both?) an X^2 and/or Y^2 term needs to be incorporated. Doesn't this then imply that X, Y, or X*Y are nonlinear? Aren't we discussing plain ol' linear models here? Doug On Tue, Sep 14, 2010 at 6:07 PM, Richard Ristow <[hidden email]> wrote: > Good points by Bruce Weaver. To comment on one of them, at 05:49 PM > 9/14/2010, he wrote: > >> d) ANOVA campers love the interaction. Traditionally, regression >> campers have not been very fond of interactions, and have gone to >> great lengths to avoid having them in their models. I suspect this >> is because they struggle to interpret what the coefficients for the >> product terms mean, and they often fail to understand that the >> coefficients for main effects are really simple main effects, etc. > > (I was, at least first, a regression camper.) > > Another reason regression-camp people stir shy of interactions is > that they're (we're) oriented toward continuous independent > variables. In a discrete-variable (classic ANOVA) model, the > 'interaction' terms fully characterize the interaction between the > factors. In a continuous-variable model, if X and Y are the > independent variables, adding X*Y doesn't remotely exhaust the ways > the two can interact. For that reason, I prefer calling X*Y a > 'cross-term' rather than an 'interaction'. > > And since X*Y is a second-order term (if both values grow in the same > proportion, it grows as the square of that proportion), including X*Y > can be taken to require including X**2 and Y**2 as well; and > suddenly, it's a much more complicated model. > > ===================== > To manage your subscription to SPSSX-L, send a message to > [hidden email] (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > For a list of commands to manage subscriptions, send the command > INFO REFCARD > ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Chow test to compare regression on two groups
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At 06:24 PM 9/14/2010, Doug wrote:
>You say that if there's an X*Y interaction term, then (either? >both?) an X^2 and/or Y^2 term needs to be incorporated. Doesn't this >then imply that X, Y, or X*Y are nonlinear? There's room for debate on this, and not everybody would agree with me. But the cross-term X*Y is non-linear, and (one line of reasoning goes) once you've included it, you can no longer argue that you've got a plain ol' linear model. And, indeed, the cross-term and square terms can sometimes get confounded in confusing ways, if you include only some of them. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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If X is linear, and Y is linear, how can X*Y be nonlinear?
On Tue, Sep 14, 2010 at 6:49 PM, Richard Ristow <[hidden email]> wrote: > At 06:24 PM 9/14/2010, Doug wrote: > >> You say that if there's an X*Y interaction term, then (either? both?) an >> X^2 and/or Y^2 term needs to be incorporated. Doesn't this then imply that >> X, Y, or X*Y are nonlinear? > > There's room for debate on this, and not everybody would agree with me. But > the cross-term X*Y is non-linear, and (one line of reasoning goes) once > you've included it, you can no longer argue that you've got a plain ol' > linear model. And, indeed, the cross-term and square terms can sometimes get > confounded in confusing ways, if you include only some of them. > > ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Chow test to compare regression on two groups
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In reply to this post by Richard Ristow
The phrase linear can mean different things in discussions of regression-type models. It can refer to the predictor variables, in which case terms in X-squared are clearly not linear. The product term X*Y would be linear in each component variable. But for purposes of statistical modeling this is fairly trivial. We could always define a new variable Z = X-squared or W = X*Y and then the model would be linear in Z or W. For purposes of statistical estimation what is more important is linearity in the coefficients. By this criterion, logistic regression or Poisson regression are not linear, even though the predictor variables may all enter linearly. David Greenberg, Sociology Department, New York University
----- Original Message ----- From: Richard Ristow <[hidden email]> Date: Tuesday, September 14, 2010 6:57 pm Subject: Re: Chow test to compare regression on two groups To: [hidden email] > At 06:24 PM 9/14/2010, Doug wrote: > > >You say that if there's an X*Y interaction term, then (either? > >both?) an X^2 and/or Y^2 term needs to be incorporated. Doesn't this > >then imply that X, Y, or X*Y are nonlinear? > > There's room for debate on this, and not everybody would agree with > me. But the cross-term X*Y is non-linear, and (one line of reasoning > goes) once you've included it, you can no longer argue that you've > got a plain ol' linear model. And, indeed, the cross-term and square > terms can sometimes get confounded in confusing ways, if you include > only some of them. > > ===================== > To manage your subscription to SPSSX-L, send a message to > [hidden email] (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > For a list of commands to manage subscriptions, send the command > INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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Hello,
This list is great, I always learn alot. Thank you all contributors. I wonder if there is any caution or argument against using and reporting BOTH Akaike (AIC) and Bayes (BIC) information criteria when comparing model fit in confirmatory factor analysis? Thanks in advance. Martin ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Chow test to compare regression on two groups
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In reply to this post by Bruce Weaver
Good morning! Here it is!
Parameter Estimates Dependent Variable:depression Parameter 95% Confidence Interval B Std. Error t Sig. Lower Bound Upper Bound Intercept -39,733 14,671 -2,708 ,008 -68,820 -10,646 coping1 -,500 ,927 -,539 ,591 -2,339 1,339 coping2 3,178 2,088 1,522 ,131 -,961 7,317 coping3 ,145 ,824 ,176 ,861 -1,489 1,779 coping4 1,884 1,161 1,623 ,107 -,417 4,185 coping5 ,446 1,321 ,338 ,736 -2,173 3,066 coping6 -1,471 1,708 -,861 ,391 -4,857 1,915 [sex=1,00] * coping1 -,058 ,967 -,060 ,952 -1,974 1,858 [sex=2,00] * coping1 0a . . . . . [sex=1,00] * coping2 -1,416 2,112 -,670 ,504 -5,602 2,771 [sex=2,00] * coping2 0a . . . . . [sex=1,00] * coping3 ,204 ,910 ,225 ,823 -1,599 2,008 [sex=2,00] * coping3 0a . . . . . [sex=1,00] * coping4 -1,824 1,103 -1,653 ,101 -4,011 ,364 [sex=2,00] * coping4 0a . . . . . [sex=1,00] * coping5 -,391 1,355 -,289 ,773 -3,077 2,295 [sex=2,00] * coping5 0a . . . . . [sex=1,00] * coping6 3,918 1,857 2,110 ,037 ,236 7,600 [sex=2,00] * coping6 0a . . . . . a. This parameter is set to zero because it is redundant. |
Re: Chow test to compare regression on two groups
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Administrator
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Hi José. This is from the model that excludes the main effect term for Sex. You need to include that term. What does it look like when you do? There should be two more rows with labels: [sex=1,00] [sex=2,00]
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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In reply to this post by Jose Rocha
Jose,
You've clearly sparked a lot of interest from several people, and my guess is, you'll continue receive useful commentary. Let me just state unequivocally that inclusion/exclusion of a main effect should NOT be determined based on whether a two-way interaction is statistically significant. In general, one should include all lower level effects when testing for upper level effects in regression modeling. There are certainly cases where exclusion of a main effect is warranted (e.g., multivariate analysis in the hierarchical modeling world), but your situation does not appear to be one of them.
Ryan
On Tue, Sep 14, 2010 at 4:29 PM, Jose Rocha <[hidden email]> wrote: Bruce: |
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