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From |
jhilbe@aol.com |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: RE: Model selection using AIC/BIC and other information criteria |

Date |
Wed, 24 Jun 2009 11:47:12 -0400 |

ESTAT-IC AIC = -2*LL + 2*k = -2(LL-k) GLM AIC = -2*LL + 2*k -2(LL - k) ---------------- = -------------- n n

. use auto,clear (1978 Automobile Data) . glm foreign mpg length, nolog fam(bin)

Variance function: V(u) = u*(1-u) [Bernoulli]

------------------------------------------------------------------------- ----- | OIM

-------------+----------------------------------------------------------- -----

------------------------------------------------------------------------- ----- . estat ic ------------------------------------------------------------------------- ----

-------------+----------------------------------------------------------- ----

------------------------------------------------------------------------- ---- Note: N=Obs used in calculating BIC; see [R] BIC note . aic AIC Statistic = .8965538 AIC*n = 66.344983 BIC Statistic = -245.2436 . abic AIC Statistic = .8965538 AIC*n = 66.344986 BIC Statistic = .9045494 BIC(Stata) = 73.257179

to the displayed -glm- values

. expand 2 (74 observations created) . glm foreign mpg length, nolog fam(bin)

------------------------------------------------------------------------- ----- | OIM

-------------+----------------------------------------------------------- -----

------------------------------------------------------------------------- ----- . estat ic ------------------------------------------------------------------------- ----

-------------+----------------------------------------------------------- ----

------------------------------------------------------------------------- ---- Note: N=Obs used in calculating BIC; see [R] BIC note . aic AIC Statistic = .8560133 AIC*n = 126.68997 BIC Statistic = -603.9058 . abic AIC Statistic = .8560133 AIC*n = 126.68996 BIC Statistic = .8600111 BIC(Stata) = 135.68161 ***

data was expanded.

sizes. This was the intent of the statistic in the first place.

adjustment for sample size, unlike the version used in -estat ic-.

table developed by Raftery for his original version of BIC.

that's another discussion. Joseph Hilbe ========================================= ate: Tue, 23 Jun 2009 22:20:36 -0500 From: Richard Williams <Richard.A.Williams.5@ND.edu>

At 08:39 PM 6/23/2009, kokootchke wrote:

Thank you, Richard. This was exactly what I thought... but I remember from my metrics classes long time ago that both AIC and BIC depend on N (sample size)... and I confirmed this by simply looking at these wikipedia entries... but, just like you, I also feared that, even though both criteria adjust for the sample size, maybe you can't compare between AICs and BICs when the models use different # of observations...

. sysuse auto, clear (1978 Automobile Data) . quietly reg price mpg trunk weight . estat ic

----

----

---- Note: N=Obs used in calculating BIC; see [R] BIC note . expand 2 (74 observations created) . quietly reg price mpg trunk weight . estat ic

----

----

---- Note: N=Obs used in calculating BIC; see [R] BIC note So, even if data are missing at random with your X variable, the smaller sample sizes that result from its inclusion will drive down the BIC and AIC stats quite a bit. - ------------------------------------------- Richard Williams, Notre Dame Dept of Sociology OFFICE: (574)631-6668, (574)631-6463 HOME: (574)289-5227 EMAIL: Richard.A.Williams.5@ND.Edu WWW: http://www.nd.edu/~rwilliam * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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