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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: positive interaction - negative covariance |

Date |
Sat, 23 Feb 2013 00:47:00 +0000 |

Correction. The code should end , ra(1 1764) On Sat, Feb 23, 2013 at 12:45 AM, Nick Cox <njcoxstata@gmail.com> wrote: > This is very confusing. > > 1. In terms of your previous statement of "a simple regression model" > you should have applied code like this, tailored to the special syntax > of -twoway function-. > > local b0 = 1.663478 > local b1 = .0021067 > local b2 = -.3692713 > local b3 = -.0010758 > > twoway function `b0' + `b1'*x, ra(1 1764) || /// > function `b0' + (`b1' + `b3')*x + `b2', x(1 1764) > > after which the functions would appear as perfect straight lines; no > jaggedness is implied. The jaggedness is a consequence of using -dur- > when only -x- is allowed and needed. -x- is a generic x axis variable > and unrelated to any variable in the dataset. > > 2. But now you are telling us that it is a flogit model, a term I > don't recognise. > > I think you won't get good help if you don't explain clearly and > consistently what you are doing. > > Nick > > On Fri, Feb 22, 2013 at 10:50 PM, andrea pedrazzani > <andrea.pedrazzani.piter@gmail.com> wrote: >> Thank you very much Nick, Jay and David. >> >> >> My -x- is -dur-, whose range is from 1 to 1764. >> I plotted the two curves as you suggested me: >> >> >> local b0 = 1.663478 >> local b1 = .0021067 >> local b2 = -.3692713 >> local b3 = -.0010758 >> >> twoway function `b0' + `b1'*dur, ra(1 1764) || /// >> function `b0' + (`b1' + `b3')*dur + `b2', ra(1 1764) >> >> >> The two functions have the same shape and are very close to each >> other. Both tend to slightly increase as -x- increases (the functions >> are really jagged, because -dur- has many values). The first one >> (where the condition Z is absent) is always a bit higher than the >> second (where the condition is present). If I am not wrong, this >> indicates that the impact of both on my dependent variable goes in the >> same (positive) direction. >> >> >> To Jay: my dependent variable is a proportion (I am using flogit) >> >> >> To David: >>> Thus, X has a positive impact on Y when Z is present and when Z is >>> absent, but those contributions are not significantly different. That >>> is, the interaction is essentially absent. >> >> Thank you for clarifying the point. Indeed, if I compare the >> confidence interval of b1 to the confidence interval of (b1+b3), they >> are not statistically different. Is it the same? In a book I read, the >> authors make this comparison. >> >> >> 2013/2/22 David Hoaglin <dchoaglin@gmail.com>: >>> Dear Andrea, >>> >>> The basis for a statement about the interaction is the estimate of b3 >>> and its standard error: After taking into account the contributions of >>> X and Z, the interaction is not significant (p = .245). >>> >>> Thus, X has a positive impact on Y when Z is present and when Z is >>> absent, but those contributions are not significantly different. That >>> is, the interaction is essentially absent. >>> >>> A negative covariance between b1 and b3 is to be expected. >>> >>> You may want to remove XZ from the model. >>> >>> Regards, >>> >>> David Hoaglin >>> >>> On Fri, Feb 22, 2013 at 12:32 PM, andrea pedrazzani >>> <andrea.pedrazzani.piter@gmail.com> wrote: >>>> Hello, >>>> >>>> I have a simple regression model with an interaction: Y = b0 + (b1)X + >>>> (b2)Z + (b3)XZ. >>>> Z is a dummy (0 or 1). >>>> >>>> b1 = .0021067 (SE= .0008513 and p=0.013) >>>> b2 = -.3692713 (SE= .2329837 and p=0.113) >>>> b3 = -.0010758 (SE= .000926 and p=0.245) >>>> >>>> Hence, the combined coefficient (i.e., the coefficient on X when Z=1) >>>> is positive: >>>> b1+b3 = .0021067 + -.0010758 = .0010309 >>>> >>>> with SE = sqrt( var(b1) + var(b3)*(Z^2) + 2Z*cov(b1,b3) ) >>>> = sqrt( .0000007246 + .0000008574*1 + -.0000007079*2 ) >>>> = .00040768 >>>> >>>> To get the p-value for the combinet coefficient, I did >>>> .0010309/.00040768 = 2.528699. The corresponding p = 0.0114. >>>> >>>> Summing up, X has a positive impact on Y when the condition Z is >>>> present (.0010309), and a positive impact also when the condition Z is >>>> not present (.0021067). >>>> So, what can I say about the interaction? What kind of interaction is >>>> it when the impact of X is positive both when the condition is present >>>> and when it is absent? Moreover, the coefficients b1 and (b1+b3) are >>>> very similar to each other. >>>> Also, both b1 and the combined coefficient (b1+b3) are positive, but >>>> the covariance between b1 and b3 is negative. It sounds strange to >>>> me... * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: positive interaction - negative covariance***From:*andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>

**References**:**st: positive interaction - negative covariance***From:*andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>

**Re: st: positive interaction - negative covariance***From:*David Hoaglin <dchoaglin@gmail.com>

**Re: st: positive interaction - negative covariance***From:*andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>

**Re: st: positive interaction - negative covariance***From:*Nick Cox <njcoxstata@gmail.com>

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