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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 00:45:22 +0000 |

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:*Nick Cox <njcoxstata@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>

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