Re: [R] Testing general hypotheses on regression coefficients
On Sunday, September 7, 2014 5:47 PM, peter dalgaard pda...@gmail.com wrote: On 06 Sep 2014, at 12:24 , bonsxanco bonsxa...@yahoo.com wrote: 1) 8th grade algebra tells me B2/B1 == 0 == B2 =0; EViews (econometrics program) doesn't have the same opinion: Wald test on my real model (edited): * H0: B3/B2 = 0 - F-stat = 37.82497 * H0: B3 = 0- F-stat = 16.31689 And when the econometrics program contradicts what you learned in 8th grade, surely the latter is wrong and the former is right, because it is done by a computer and computers cannot be wrong? ;-) I simply thought that there was a standard way to do this: EViews and Stata both give the exact same F statistic for my original problem. Given that these programs were not developed by the same author (AFAIK), there is some specific way to reformulate the restriction which make EViews and Stata give the same answer. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
On Monday, September 8, 2014 6:46 PM, Greg Snow 538...@gmail.com wrote: [very good suggestions] Thank you Greg for dedicating some time to my problem and giving advice on how I can tackle the issue. It is very appreciated. Unfortunately I think I will use another program for my original problem. Anyway, I'll go through all your suggestions, time permitting. Best, Chris __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
Others have discussed some of the theoretical approaches (delta method), but as has also been pointed out, this is a mailing list about R, not theory, so here are some approaches to your question from the approach of those of us who like programming R more than remembering theory. I assume that one reason you may be interested in B2/B1 is that you want the confidence interval on the quantity, not just the test of whether it is 0 (that test being equivalent to B2=0 unless B1 is exactly equal to 0). So I will focus more on confidence intervals (which you can use as tests by seeing if the null value is in the interval/region or not). Approach 1, simulation: If all the assumptions hold for the linear regression, then the parameter estimates are considered to by multivariate normal. You can get the covariance matrix for this normal using the vcov function on the summary of your fitted object. Now you can use the mvrnorm function with the estimated means and covariance to generate a bunch of observations from this multivariate normal and compute B2/B1 or some combination of B2/B1 and B4/B3 for each observation. These values represent the distribution of interest and you can calculate a confidence interval by finding the quantiles of the values (0.025 and 0.975 for 95%) or finding the HPD interval (minimum width interval), the emp.hpd function in the TeachingDemos package is one way to do this. For your second hypothesis you could look at B2/B1 - B4/B3 = 0 or (B2/B1) / (B4/B3) = 1, or create a joint confidence region on the 2 ratios and see if the x=y line intersects that region. Approach 2, bootstrap: Bootstrap the whole process, fit the regression model then find the ratio of the estimates. Find the bootstrap confidence interval of the ratio(s), follow above advice. Approach 3, Bayes: Fit a Bayesian regression model and look at the posterior distribution of the ratio(s) of interest, calculate the credible interval/region (the steps will be similar to the previous approaches). Approach 4, simulate from the null: Fit your regression model under then null hypothesis of interest being true (for a more complicated null, your second, you may need to use optimization or quadratic programming to allow some values to vary, but have others dependent on those, then find the least squares solution). Now simulate data based on that model, fit the full regression to the simulated data sets and compare the parameter estimates (or ratios thereof) to the parameter estimates from the original data. You could try any of these approaches for hypotheses where traditional linear hypotheses work and compare the results from the traditional approach to the above approaches to see how they compare (and how many iterations/samples you will need). On Fri, Sep 5, 2014 at 8:17 PM, Chris bonsxa...@yahoo.com wrote: Hi. Say I have a model like y = a + B1*x1 + B2*x2 + B3*x3 + B4*x4 + e and I want to test H0: B2/B1 = 0 or H0: B2/B1=B4/B3 (whatever H1). How can I proceed? I now about car::linearHypothesis, but I can't figure out a way to do the tests above. Any hint? Thanks. C __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Gregory (Greg) L. Snow Ph.D. 538...@gmail.com __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
On 06 Sep 2014, at 12:24 , bonsxanco bonsxa...@yahoo.com wrote: 1) 8th grade algebra tells me B2/B1 == 0 == B2 =0; EViews (econometrics program) doesn't have the same opinion: Wald test on my real model (edited): * H0: B3/B2 = 0 - F-stat = 37.82497 * H0: B3 = 0- F-stat = 16.31689 And when the econometrics program contradicts what you learned in 8th grade, surely the latter is wrong and the former is right, because it is done by a computer and computers cannot be wrong? ;-) Probably what this shows most of all is a weakness of the Wald test approach: The s.e. of (b3hat/b2hat) will likely differ from s.e.(b3hat)/b2hat and hence the test statistics will differ even though they really test the same hypothesis. Actually, there are two generic weaknesses: (a) the somewhat arbitrary choice of test statistic and (b) the fact that the s.e. is not calculated at the null value of the parameter, but at the estimate. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd@cbs.dk Priv: pda...@gmail.com __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
Hi Chris, On Fri, Sep 5, 2014 at 7:17 PM, Chris bonsxa...@yahoo.com wrote: Hi. Say I have a model like y = a + B1*x1 + B2*x2 + B3*x3 + B4*x4 + e and I want to test H0: B2/B1 = 0 As noted by Bert, think about this. or H0: B2/B1=B4/B3 (whatever H1). How can I proceed? I now about car::linearHypothesis, but I can't figure out a way to do the tests above. Any hint? Take a look at car::deltaMethod. I suggest you study the theory of the delta method. If you happen to have taken a graduate statistics/econometrics class it should not be difficult and can provide some insights. If not, at least consider that the delta method can lead to misleading estimates (biased standard errors) in many cases for finite samples. You might want to run some simulations to get a feel for it. Best, Scott -- Scott Kostyshak Economics PhD Candidate Princeton University __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
Hi. First of all, thanks to all who have replied. 1) 8th grade algebra tells me B2/B1 == 0 == B2 =0; EViews (econometrics program) doesn't have the same opinion: Wald test on my real model (edited): * H0: B3/B2 = 0 - F-stat = 37.82497 * H0: B3 = 0- F-stat = 16.31689 2) I suspect you would need to provide more context for the other The context is this: I'm estimating a model which is: d(y) = a + B1*y(-1) + B2*X_p(-1) + B3*X_n(-1) + other + error where X_p and X_n are partial sum decompositions of positive and negative shocks: X_p(t) = X_p(t-1) + (d(X_p(t))0)*d(X_p(t)) ; X_p(0)=0 X_n(t) = X_n(t-1) + (d(X_n(t))0)*d(X_n(t)) ; X_p(0)=0 I think this is enough, but I can provide the full references. Now, back to the problem: testing B2/B1=0 tells me about that the long term effect, while testing for B2/B1=B3/B1 tells me that about the equality of long term effects to negative and positive shocks. car::deltaMethod I just gave a quick look and searched about delta method, but I can't see how it would help in testing the restrictions above. I'll read more about it, though, as it seems interesting, thanks for the pointer. (Sorry if this e-mail goes out of context, but the first time I sent it through gmane, as I wasn't subscribed.) Chris __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
Scott said: car::deltaMethod I said: I just gave a quick look and searched about delta method, but I can't see how it would help in testing the restrictions above. Actually it seems that it should be the way to go: I just noticed under the EViews Wald test window the message Delta method computed using analytic derivatives. Anyway, I wonder if there's some easier way to do it. Best, Chris __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
AFAICS you are not testing a linear hypothesis (which is of the form Lb=b0 where L is a matrix and b=(a,B1,B2,B3,B3) is the parameter vector). If, for simplicity, your model is E(y) = a + bx then -a/b is the x-value for which y is zero. When you turn to estimates then u = -a/b is the ratio of two (typically correlated) normal variables and such a ratio is *not* normal. (Just think of the Cauchy distribution.) One approach is to calculate the approximate variance of u and then construct a Wald test or similar while hoping for the best. Alternatively one could perhaps try with a parametric bootstrap test. Just ideas. Good luck. Søren -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Chris Sent: 6. september 2014 04:17 To: r-h...@stat.math.ethz.ch Subject: [R] Testing general hypotheses on regression coefficients Hi. Say I have a model like y = a + B1*x1 + B2*x2 + B3*x3 + B4*x4 + e and I want to test H0: B2/B1 = 0 or H0: B2/B1=B4/B3 (whatever H1). How can I proceed? I now about car::linearHypothesis, but I can't figure out a way to do the tests above. Any hint? Thanks. C __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Testing general hypotheses on regression coefficients
Well: 1) 8th grade algebra tells me B2/B1 == 0 == B2 =0; 2) I suspect you would need to provide more context for the other, as you may be going about this entirely incorrectly (have you consulted a local statistician?): your nonlinear hypothesis probably can be made linear under the right parametrization, but context might suggest something entirely different than the approach that motivated your query. 3) But forget all that! -- this is a list about the R language, not statistics -- which seems to be the essence of your query -- although I grant that the intersection is nonempty. But for statistics help, you should try a statistics list like stats.stackexchange.com instead. Cheers, Bert Bert Gunter Genentech Nonclinical Biostatistics (650) 467-7374 Data is not information. Information is not knowledge. And knowledge is certainly not wisdom. Clifford Stoll On Fri, Sep 5, 2014 at 7:17 PM, Chris bonsxa...@yahoo.com wrote: Hi. Say I have a model like y = a + B1*x1 + B2*x2 + B3*x3 + B4*x4 + e and I want to test H0: B2/B1 = 0 or H0: B2/B1=B4/B3 (whatever H1). How can I proceed? I now about car::linearHypothesis, but I can't figure out a way to do the tests above. Any hint? Thanks. C __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
