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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 15:25:22 +0000 |

What you now describe is quite different from what you explained at the outset: you had -- it is all here in the thread -- a simple regression with just x z x*z as predictors; now it's a -glm- with logit link and extra predictors. With just x z x*z as predictors, you can plot the implied straight lines directly with -twoway function-. For a more complicated model you will need the more complex machinery of -margins- and -marginsplot-. It's still true, as David underlined, that if the terms using interactions are not significant at conventional levels, the interaction can't be regarded as well established. A quite separate point is this. As the Statalist FAQ explains, you are assumed to use Stata 12 unless you explain otherwise; that being so, advice is not to mix -xi:- and factor variable notation in an up-to-date Stata. Nick On Sat, Feb 23, 2013 at 10:58 AM, andrea pedrazzani <andrea.pedrazzani.piter@gmail.com> wrote: > Sorry, I misunderstoond the syntax. If I do as you suggest (using > -x-), I have two straight line, both with almost the same positive > slope. The first one (where the condition Z is absent) has a bit > higher intercept and is slightly steeper than the second (where the > condition is present). > > As for the model, I meant a fractional logit. I am using > > xi: glm DEPVAR X Z X*Z other-covariates i.fixed-effects, > family(binomial) r > > where DEPVAR is a fractional response variable. > > > Best, > Andrea > > 2013/2/23 Nick Cox <njcoxstata@gmail.com>: >> 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:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: positive interaction - negative covariance***From:*Maarten Buis <maartenlbuis@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>

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

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

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