[EMAIL PROTECTED] wrote:
> snip"
>
> Gus Gassmann" <[EMAIL PROTECTED]> wrote in message
> [EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> >But I was not the first to so challenge. Nunnally called
> > > normally sampled causes "dead data." Only the effects should be sampled
> as
> > > normal or triangular.
> >
> > My ignorance shows, since I have no clue as to who Nunnally was.
> > At any rate, I think he is quite wrong. My problem with his position
> > is that it _presupposes_ that I know what are the causes and the
> > effects. If I then want to use CR to classify my variables, that is
> > circular logic.
>
> Nunnally wrote some good books on statistics and psychometrics.
>
> You will not know the causes and effects but you can hypothesize them. Let's
> say you think variable A causes variable B. But A is normally distributed.
> Then predict A from B and use the residual as an estimation of latent causes
> L. Put A, L and B in a spread sheet. Sort by A, the hypothesized cause.
> Trim off all A values and corresponding values in L and B that are above
> zA+1.7. Then trim off the values below zA -1.7. Then sort by L. Trim off
> the values of A, L and B corresponding to zL above zL=1.7 and below zL=-1.7.
> Now your causes have been trimmed so that they are close enough to uniform
> to allow similar extremes of A and L to occur together. Conduct CR on this
> trimmed data. If rde is negative then B is a cause of A.
>
> If you wish to check for reverse causation or to make sure A doesnot also
> cause B, then predict B from A, obtain the new residual LL and trim by B and
> LL.
>
> If you get a chance, read Nunnally's classic text Psychometrics.
>
> Bill
Fine. In the meantime, can you help me out on my two datasets below?
> > Here are two data sets for you:
> >
> > Sample 1 Sample 2
> > x1 x2 x3 x1 x2 x3
> > -0.1080 0.3953 0.5033 -0.4397 0.2960 -0.1437
> > -0.0397 -0.4221 -0.3824 0.1654 -0.0392 0.1262
> > 0.1731 -0.3578 -0.5309 -0.1806 -0.3556 -0.5362
> > -0.1922 -0.3609 -0.1687 0.3486 -0.2583 0.0903
> > -0.4954 0.0686 0.5640 -0.3397 -0.2943 -0.6340
> > 0.1204 0.2726 0.1522 0.2225 0.2985 0.5210
> > 0.2326 -0.1835 -0.4161 0.4383 0.1177 0.5560
> > 0.0382 -0.1677 -0.2059 0.4894 -0.1643 0.3251
> > 0.1101 -0.2875 -0.3976 0.2245 0.3840 0.6085
> > 0.2314 -0.0712 -0.3026 -0.1449 -0.1220 -0.2669
> > 0.1834 -0.0154 -0.1988 0.3106 -0.3532 -0.0426
> > -0.3144 -0.3424 -0.0280 -0.0671 -0.2752 -0.3423
> > -0.1609 -0.1717 -0.0108 -0.0526 0.1395 0.0869
> > -0.3071 -0.0672 0.2399 -0.0737 -0.4318 -0.5055
> > 0.3023 0.3298 0.0275 -0.4424 -0.1317 -0.5741
> > -0.3086 -0.1721 0.1365 -0.2790 -0.3178 -0.5968
> > -0.0301 0.4549 0.4850 0.1514 0.2256 0.3770
> > -0.4170 0.4049 0.8219 0.3591 -0.1085 0.2506
> > 0.3822 0.4298 0.0476 0.0932 -0.3287 -0.2355
> > 0.4678 -0.3920 -0.8598 -0.2843 0.3962 0.1119
> > -0.3454 0.4602 0.8056 -0.1186 0.0616 -0.0570
> > -0.1997 -0.4107 -0.2110 0.3543 0.4832 0.8375
> > -0.0753 -0.2161 -0.1408 -0.0579 -0.3364 -0.3943
> > 0.4514 0.3021 -0.1493 0.0820 0.4140 0.4960
> > -0.4914 0.1282 0.6196 0.0238 0.2010 0.2248
> > -0.3188 -0.2597 0.0591 -0.4660 -0.0083 -0.4743
> > 0.0954 -0.4192 -0.5146 0.3160 0.1450 0.4610
> > 0.3109 -0.1859 -0.4968 0.2707 -0.3065 -0.0358
> > 0.1177 0.0425 -0.0752 -0.1334 -0.4000 -0.5334
> > 0.0988 0.0866 -0.0122 0.3131 0.0778 0.3909
> > 0.2042 -0.3173 -0.5215 0.1473 -0.3525 -0.2052
> > 0.4936 0.0075 -0.4861 0.1552 0.3760 0.5312
> > 0.3995 0.1239 -0.2756 -0.4542 0.3861 -0.0681
> > -0.2928 0.1044 0.3972 -0.1404 0.3967 0.2563
> > -0.2079 -0.4417 -0.2338 0.0219 -0.1143 -0.0924
> > -0.2872 0.2315 0.5187 -0.2758 0.0582 -0.2176
> > 0.0952 0.2241 0.1289 0.1723 0.1686 0.3409
> > 0.0612 0.4615 0.4003 0.0937 -0.4729 -0.3792
> > 0.0994 -0.3605 -0.4599 -0.0574 0.0202 -0.0372
> > -0.2700 -0.0366 0.2334 0.0330 0.1393 0.1723
> > 0.2352 -0.2092 -0.4444 -0.1287 0.4526 0.3239
> > -0.3092 0.3306 0.6398 0.4807 -0.4881 -0.0074
> > -0.3007 0.2191 0.5198 0.1418 0.0555 0.1973
> > -0.0645 -0.1181 -0.0536 -0.1412 0.2659 0.1247
> > 0.1709 -0.1709 -0.3418 0.0594 -0.2961 -0.2367
> > 0.4761 0.4055 -0.0706 -0.4084 -0.3958 -0.8042
> > -0.4904 0.2683 0.7587 -0.3724 0.4771 0.1047
> > -0.2681 0.0731 0.3412 -0.0559 -0.0793 -0.1352
> > -0.0226 0.2264 0.2490 -0.0836 0.2387 0.1551
> > 0.1847 0.1867 0.0020 0.2396 0.0202 0.2598
> > 0.2076 0.2120 0.0044 -0.3015 0.0792 -0.2223
> > 0.2451 0.4303 0.1852 -0.3462 0.3331 -0.0131
> > -0.0490 -0.0084 0.0406 -0.1550 -0.0568 -0.2118
> > -0.0365 -0.3069 -0.2704 -0.3262 -0.3329 -0.6591
> > 0.2611 0.3574 0.0963 0.4767 0.2800 0.7567
> > -0.0611 0.1078 0.1689 -0.1874 -0.2461 -0.4335
> > -0.1591 -0.0597 0.0994 0.0916 0.0904 0.1820
> > 0.3689 -0.2308 -0.5997 -0.4325 0.0419 -0.3906
> > 0.2228 -0.4240 -0.6468 -0.4178 -0.4326 -0.8504
> > 0.4775 -0.2383 -0.7158 0.4032 -0.2920 0.1112
> > 0.3783 -0.0090 -0.3873 0.3121 0.2828 0.5949
> > -0.0566 0.0260 0.0826 0.3388 0.3410 0.6798
> > 0.4026 0.1592 -0.2434 0.0499 0.3937 0.4436
> > -0.1845 0.1619 0.3464 -0.2070 -0.2163 -0.4233
> > -0.2490 -0.1894 0.0596 0.1267 0.4613 0.5880
> > 0.3668 -0.3443 -0.7111 -0.0371 0.4682 0.4311
> > -0.4651 -0.0808 0.3843 -0.0616 0.3536 0.2920
> > 0.3750 0.0377 -0.3373 0.2678 -0.0612 0.2066
> > -0.1645 -0.2539 -0.0894 0.0980 -0.0522 0.0458
> > 0.4041 -0.1345 -0.5386 -0.2904 -0.0675 -0.3579
> > 0.0645 -0.2520 -0.3165 0.1373 -0.1961 -0.0588
> > 0.0621 0.3327 0.2706 -0.1248 0.1215 -0.0033
> > -0.1591 0.4404 0.5995 -0.3287 -0.4614 -0.7901
> > 0.1182 -0.4835 -0.6017 -0.3457 0.2191 -0.1266
> > -0.2415 -0.2480 -0.0065 0.2812 0.4961 0.7773
> > -0.3003 -0.4429 -0.1426 0.1968 -0.2689 -0.0721
> > 0.1662 0.3290 0.1628 -0.4027 0.4364 0.0337
> > -0.2538 0.4813 0.7351 0.4085 0.3003 0.7088
> > 0.2485 0.1853 -0.0632 -0.3424 -0.1506 -0.4930
> > -0.2859 -0.3326 -0.0467 -0.2163 0.4987 0.2824
> > -0.1710 0.0792 0.2502 -0.2549 0.2514 -0.0035
> > 0.0548 -0.0992 -0.1540 -0.0244 -0.1422 -0.1666
> > 0.0410 0.1996 0.1586 0.4855 0.4630 0.9485
> > 0.3219 0.2388 -0.0831 0.3642 -0.0608 0.3034
> > 0.4776 0.2809 -0.1967 -0.3695 -0.0575 -0.4270
> > -0.0407 0.3851 0.4258 0.2506 -0.2512 -0.0006
> > -0.3385 0.0563 0.3948 -0.2974 -0.4193 -0.7167
> > 0.3362 -0.4555 -0.7917 -0.4036 -0.2230 -0.6266
> > -0.4863 -0.3058 0.1805 0.2822 -0.1218 0.1604
> > -0.3244 0.1590 0.4834 -0.2181 0.1220 -0.0961
> > -0.2982 0.3868 0.6850 -0.4685 0.1107 -0.3578
> > -0.4723 -0.1808 0.2915 0.4669 0.0894 0.5563
> > -0.4189 -0.2992 0.1197 -0.3594 0.1894 -0.1700
> > 0.1484 0.4720 0.3236 0.4702 -0.3301 0.1401
> > 0.4847 -0.4153 -0.9000 0.4001 -0.0267 0.3734
> > -0.4401 0.3119 0.7520 0.2147 -0.4939 -0.2792
> > 0.2471 0.0177 -0.2294 0.3135 -0.4004 -0.0869
> > -0.1915 0.2655 0.4570 0.2022 0.1466 0.3488
> > -0.4083 -0.4815 -0.0732 0.1384 -0.4058 -0.2674
> > 0.4440 -0.0507 -0.4947 -0.2001 -0.1060 -0.3061
> >
> > In both samples the columns marked x1 and x2 are uniformly distributed
> > on [-0.5, +0.5]. (Reasonably closely, anyway: the data are set up so that
> > there will be one (x1,x2) in [-0.5,-0.4]x[-0.5,-0.4], one in
> > [-0.5,-0.4]x[-0.4,-0.3],
> > one in [-0.5,-0.4]x[-0.3,-0.2], and so on, for the obvious partition of
> > [-0.5,+0.5]x[-0.5,+0.5] into 100 smaller squares of side 0.1. So they do
> > fill the square, as you requested.)
> >
> > Both, in fact are subsets of larger samples, and I can
> > send you the full files if interested --- there is not enough room here.
> > In both samples the three columns are connected via x3 = x1 + x2.
> > However, in one of the two samples x3 is in fact computed in this way,
> > caused by the other two, the way I use the word, whereas in the other
> > sample x1 and x3 are originally generated (uniformly) and then x2
> > is calculated as x2 = x3 - x1, in other words, x2 is the _effect_.
> > Can you tell them apart?
> >
> > > Sampling is a type of perception and like all perception, the instrument
> is
> > > a construction. The eyes do not allow us to see many wave lengths. We
> are
> > > subject to certain illusions. The eyes are not perfect. No sampling
> strategy
> > > is perfect either. Only God in his omniscience has perfect perception.
> We
> > > ain't him. Neither is the normal distribution.
> >
> > > When we collect an approximately equal number AND a sufficient number of
> > > observations so that we can see the combinations of all the possible
> values
> > > of the causes, then we get a less distorted view of how those causes can
> > > combine. The manifold is a map or prototype of such structure. A cause
> can
> > > be expressed in data but unless we can see it, we can not make much
> sense of
> > > it. This is why scientists search long and hard to fill out the ranges
> of
> > > their observations in experimental science. Normal distributions do not
> > > reflect the combinations of the similar extremes of causes. You do not
> see
> > > normally distributed cell sizes across the factors of an ANOVA. We need
> > > something else to see what happens in the extremes of the
> > > cross-tabulation/conjunction of causes. This something else is a
> manifold,
> > > which is approximated by uniform samples of the causes.
> > >
> > > Bill
> >
.
.
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