Okay. I didn't post the table with the correlation coefficient as it seemed a bit "overkill".
Thank you, I will try the proposed method.
Thank you, I will try the proposed method.
-
Login or Register
- Log in with
- You are not logged in. You can browse but not post. Login or Register by clicking 'Login or Register' at the top-right of this page. For more information on Statalist, see the FAQ.
-
-
I have had time to return to the data, and I had some colleagues look at it as well. We have not been able to solve this issue. This is why I am returning to your comment, William with some follow-up questions.
Here is the entire output from the tetrachoric command
A colleague of mine noticed that the correlation between network and competition is -1. Using the polychoric command, this correlation coefficient equals 0.0. I understand now, why you requested the entire output. It turns out that there are no observations in the dataset that have both networking activities and hosts competitions, Can this be why I get the error message? I tried recoding competition so that the competition=1/network=1 combination was represented in the dataset, i do, however, still get the above error message.Code:tetrachoric requirement funding competition discussion event citizen_science cam > paign platform training guiding rules policy network unit strategy standard coop > eration res_area sup_res sup_ed (obs=217) matrix with tetrachoric correlations is not positive semidefinite; it has 5 negative eigenvalues maxdiff(corr,adj-corr) = 0,3721 (adj-corr: tetrachoric correlations adjusted to be positive semidefinite) | requir~t funding compet~n discus~n event citize~e campaign -------------+--------------------------------------------------------------- requirement | 1,0000 funding | 0,4324 1,0000 competition | -0,0793 0,3978 1,0000 discussion | 0,2243 -0,1203 -0,0237 1,0000 event | -0,0324 0,5958 0,6756 0,1967 1,0000 citizen_sc~e | 0,1179 0,7278 0,0196 0,0858 0,7500 1,0000 campaign | -0,0662 0,5213 -0,0535 0,1996 0,6992 0,7144 1,0000 platform | 0,0072 -0,0525 0,3951 0,0028 0,4322 0,3194 0,0325 training | -0,1158 0,4146 0,4114 0,4036 0,4363 0,1631 0,1344 guiding | -0,0856 0,1019 -0,1200 0,0301 -0,0822 0,1609 0,2408 rules | 0,5276 0,2780 -0,3215 0,1724 -0,1953 -0,0759 -0,1423 policy | 0,3280 0,0655 0,0826 0,4743 0,4133 0,2716 0,4290 network | 0,2335 -0,0340 -1,0000 0,5163 0,1251 0,1201 0,1619 unit | 0,0249 -0,1447 0,4409 0,0978 0,4082 -0,0638 -0,0774 strategy | 0,3853 0,3276 0,3085 0,1831 0,2463 0,4806 0,1703 standard | 0,3935 -0,0214 -0,1923 -0,1689 -0,3900 -0,2688 -0,1765 cooperation | 0,3161 0,4847 -0,0482 0,3448 0,5356 0,7006 0,7144 res_area | 0,1842 0,7106 0,1242 -0,1252 0,5347 0,7205 0,5274 sup_res | 0,5837 0,5239 -0,1151 0,1727 0,1608 0,0809 0,1774 sup_ed | 0,3814 0,5254 0,2286 0,0858 0,3090 -0,2188 0,1445 | platform training guiding rules policy network unit -------------+--------------------------------------------------------------- platform | 1,0000 training | 0,2358 1,0000 guiding | -0,0352 -0,1662 1,0000 rules | -0,0759 0,0277 0,0701 1,0000 policy | 0,2716 0,3622 0,0701 0,0145 1,0000 network | 0,2362 0,4568 0,0614 0,4572 0,7082 1,0000 unit | 0,3637 0,1421 0,1180 -0,0419 -0,0419 0,1168 1,0000 strategy | 0,0485 0,0263 0,3949 0,0036 -0,1743 0,0887 0,3676 standard | -0,0065 0,0206 0,2743 0,4876 0,2042 0,1660 -0,0323 cooperation | 0,2833 0,5182 0,3405 0,1989 0,6876 0,7500 0,1872 res_area | 0,1416 0,4321 0,3638 0,2500 0,3215 0,1607 -0,0112 sup_res | -0,0281 0,3880 -0,1474 0,7382 0,2875 0,2829 0,0360 sup_ed | -0,2188 0,4902 0,1609 0,1728 0,4389 0,2362 0,0175 | strategy standard cooper~n res_area sup_res sup_ed -------------+------------------------------------------------------ strategy | 1,0000 standard | 0,3688 1,0000 cooperation | 0,3327 0,1095 1,0000 res_area | 0,4191 -0,0972 0,6530 1,0000 sup_res | 0,1619 0,4269 0,5665 0,3928 1,0000 sup_ed | -0,0829 0,3397 0,5830 0,0466 0,6018 1,0000 . matrix r = r(Rho) . factormat r, n(217) r not positive (semi)definite r(506); end of do-file r(506);
The problem can be solved with the ,posdef option as you mentioned, but what does this mean? is this legitimate? I am highly confused as I did a similar analysis on other variables in the dataset, which are also all binary. These are on which understandings of responsibility the oranizations worked with and this worked just fine with the polychoricpca and tetrachoric varlist, matrix r = r(Rho)The requirement that the correlation matrix input to principle components analysis be positive semidefinite is a serious statistical concern, so the error message from factormat about the correlation matrix from tetrachoric is important.
factormat r, n(217). However, these two methods - that yield the same correlation coefficients - suggest three dimensions for the first method and 5 dimensions for the latter. I belive it should be similar? These analyses are done with all 217 observations in the dataset. I hope you can help me, I am on the verge of quitting this factor analysis all together.Last edited by Malene Christensen; 18 Jul 2017, 08:01.Comment
-
Reviewing the documentation in help polychoricpca and help factormat and help pca suggests that you are comparing apples with oranges. polychoricpca produces a principle components analysis, whereas factormat produces a factor analysis, by default using the principal-factor method, although optionally using the principle-component factor method.andCode:polychoricpca
... these two methods - that yield the same correlation coefficients - suggest three dimensions for the first method and 5 dimensions for the latter. I belive it should be similar?Code:tetrachoric varlist matrix r = r(Rho) factormat r, n(217)
I think that to be comparable to polychoricpca, you would have to use the pca command rather than the factormat command. Or conversely, going back to your post #1, since you want a factor analysis, polychoricpca is not the tool for you; factormat is. However, it is possible that
would produce results more similar to those from polychoricpca.Code:factormat r, n(217) pcf
Comment
-
Wow, I have indeed confused these terms! Thank you for clearing this up! I believe that the Principal Component Analysis is the most correct to use in this case, as the primary purpose is data reduction in an explorative out-set. So I need a polychoric PCA - which does not work or I could try to store the tetrachoric/polychoric correlation coefficients and do a pcamat, which also does not work.
Code:polychoricpca requirement funding competition discussion event citizen_science c > ampaign platform training guiding rules policy network unit strategy standard co > operation res_area sup_res sup_ed could not calculate numerical derivatives missing values encountered could not calculate numerical derivatives missing values encountered Polychoric correlation matrix requirement funding competition requirement 1 funding ,43360211 1 competition -,07963118 ,39906673 1 discussion ,22511135 -,12062146 -,02376225 event -,03243606 ,59658092 ,67674132 citizen_science ,11872629 ,72926096 ,01991276 campaign -,06642385 ,52262024 -,05369341 platform ,00737133 -,05270511 ,39700047 training -,1162005 ,41540034 ,41257345 guiding -,08579849 ,10211343 -,12030967 rules ,52943032 ,2791685 -,32344164 policy ,32958669 ,06590443 ,08317795 network ,23488741 -,03405168 . unit ,02502208 -,14509878 ,44205054 strategy ,38606621 ,32795366 ,30917024 standard ,39458861 -,02141349 -,19300705 cooperation ,31689848 ,48534115 -,04827437 res_area ,18502194 ,71155498 ,12484554 sup_res ,58525384 ,52510344 -,11564683 sup_ed ,38322625 ,52704529 ,22991512 discussion event citizen_science discussion 1 event ,19717124 1 citizen_science ,08629164 ,75138492 1 campaign ,20043572 ,70035335 ,71610885 platform ,00290081 ,43367535 ,32136945 training ,40441367 ,43696061 ,1639602 guiding ,03021667 -,08227838 ,16150499 rules ,17318865 -,19611518 -,0762605 policy ,47571215 ,41453787 ,27321665 network ,51792978 ,12572792 ,12105779 unit ,09806615 ,40882123 -,0639711 strategy ,18334256 ,24649133 ,48180778 standard -,16930525 -,39110504 -,27012386 cooperation ,34534373 ,53610536 ,70199426 res_area -,1256119 ,53572544 ,72206206 sup_res ,17333193 ,16136692 ,08144885 sup_ed ,08629164 ,31020763 -,22033115 campaign platform training campaign 1 platform ,03285636 1 training ,13500998 ,23688703 1 guiding ,24149222 -,03522224 -,16647947 rules -,14311739 -,0762605 ,02786731 policy ,43079963 ,27321665 ,36346845 network ,16301905 ,23786434 ,45842578 unit -,07768877 ,36506261 ,14251282 strategy ,17071145 ,04870872 ,02642428 standard -,17717211 -,00640102 ,02070659 cooperation ,71552201 ,28435191 ,51882571 res_area ,52891711 ,14245858 ,43315516 sup_res ,17836936 -,02810993 ,38906015 sup_ed ,14547083 -,22033115 ,49178715 guiding rules policy guiding 1 rules ,07038232 1 policy ,07038232 ,01469897 1 network ,06168779 ,45937531 ,71012239 unit ,11815959 -,04198881 -,04198881 strategy ,39487928 ,0036789 -,1747876 standard ,27461083 ,4889252 ,20498582 cooperation ,3407695 ,19958837 ,68885162 res_area ,36451458 ,25116821 ,32285854 sup_res -,14781197 ,73962198 ,28886311 sup_ed ,16150499 ,17401462 ,4409355 network unit strategy network 1 unit ,11746568 1 strategy ,08910018 ,36786705 1 standard ,16677031 -,03233762 ,36906466 cooperation ,75144149 ,18751041 ,33280116 res_area ,16164549 -,01119367 ,41976814 sup_res ,28442846 ,0362096 ,16230451 sup_ed ,23786434 ,01768492 -,08308129 standard cooperation res_area standard 1 cooperation ,10972283 1 res_area -,09751973 ,65382663 1 sup_res ,42791047 ,56748995 ,39403875 sup_ed ,34095752 ,58448547 ,04701396 sup_res sup_ed sup_res 1 sup_ed ,60365551 1 matrix symeigen: matrix has missing values r(504);If I exclude either the Network variable or the Competition variable, it works, which is highly perculiar! The only odd thing here is, as already mentioned, that there are no observations in the dataset which score 1 on both there variables:Code:. tetrachoric requirement funding competition discussion event citizen_science cam > paign platform training guiding rules policy network unit strategy standard coop > eration res_area sup_res sup_ed (obs=217) matrix with tetrachoric correlations is not positive semidefinite; it has 5 negative eigenvalues maxdiff(corr,adj-corr) = 0,3721 (adj-corr: tetrachoric correlations adjusted to be positive semidefinite) | requir~t funding compet~n discus~n event citize~e campaign -------------+--------------------------------------------------------------- requirement | 1,0000 funding | 0,4324 1,0000 competition | -0,0793 0,3978 1,0000 discussion | 0,2243 -0,1203 -0,0237 1,0000 event | -0,0324 0,5958 0,6756 0,1967 1,0000 citizen_sc~e | 0,1179 0,7278 0,0196 0,0858 0,7500 1,0000 campaign | -0,0662 0,5213 -0,0535 0,1996 0,6992 0,7144 1,0000 platform | 0,0072 -0,0525 0,3951 0,0028 0,4322 0,3194 0,0325 training | -0,1158 0,4146 0,4114 0,4036 0,4363 0,1631 0,1344 guiding | -0,0856 0,1019 -0,1200 0,0301 -0,0822 0,1609 0,2408 rules | 0,5276 0,2780 -0,3215 0,1724 -0,1953 -0,0759 -0,1423 policy | 0,3280 0,0655 0,0826 0,4743 0,4133 0,2716 0,4290 network | 0,2335 -0,0340 -1,0000 0,5163 0,1251 0,1201 0,1619 unit | 0,0249 -0,1447 0,4409 0,0978 0,4082 -0,0638 -0,0774 strategy | 0,3853 0,3276 0,3085 0,1831 0,2463 0,4806 0,1703 standard | 0,3935 -0,0214 -0,1923 -0,1689 -0,3900 -0,2688 -0,1765 cooperation | 0,3161 0,4847 -0,0482 0,3448 0,5356 0,7006 0,7144 res_area | 0,1842 0,7106 0,1242 -0,1252 0,5347 0,7205 0,5274 sup_res | 0,5837 0,5239 -0,1151 0,1727 0,1608 0,0809 0,1774 sup_ed | 0,3814 0,5254 0,2286 0,0858 0,3090 -0,2188 0,1445 | platform training guiding rules policy network unit -------------+--------------------------------------------------------------- platform | 1,0000 training | 0,2358 1,0000 guiding | -0,0352 -0,1662 1,0000 rules | -0,0759 0,0277 0,0701 1,0000 policy | 0,2716 0,3622 0,0701 0,0145 1,0000 network | 0,2362 0,4568 0,0614 0,4572 0,7082 1,0000 unit | 0,3637 0,1421 0,1180 -0,0419 -0,0419 0,1168 1,0000 strategy | 0,0485 0,0263 0,3949 0,0036 -0,1743 0,0887 0,3676 standard | -0,0065 0,0206 0,2743 0,4876 0,2042 0,1660 -0,0323 cooperation | 0,2833 0,5182 0,3405 0,1989 0,6876 0,7500 0,1872 res_area | 0,1416 0,4321 0,3638 0,2500 0,3215 0,1607 -0,0112 sup_res | -0,0281 0,3880 -0,1474 0,7382 0,2875 0,2829 0,0360 sup_ed | -0,2188 0,4902 0,1609 0,1728 0,4389 0,2362 0,0175 | strategy standard cooper~n res_area sup_res sup_ed -------------+------------------------------------------------------ strategy | 1,0000 standard | 0,3688 1,0000 cooperation | 0,3327 0,1095 1,0000 res_area | 0,4191 -0,0972 0,6530 1,0000 sup_res | 0,1619 0,4269 0,5665 0,3928 1,0000 sup_ed | -0,0829 0,3397 0,5830 0,0466 0,6018 1,0000 . matrix r = r(R) . pcamat r, n(217) matrix r has missing values r(504); end of do-file r(504);
I don't understand, however, why this should be a problem to the PCA on tetrachoric coefficients? Can anyone enlighten me on this?Code:| competition network | 0 1 | Total -----------+----------------------+---------- 0 | 168 28 | 196 1 | 21 0 | 21 -----------+----------------------+---------- Total | 189 28 | 217Last edited by Malene Christensen; 19 Jul 2017, 03:41.Comment
-
In general, when working with categorical variables like network and competition, if knowing that in your data one of the variables has a particular value (e.g. network=1) allows you to state that another variable has a particular value (e.g. competition=0), the methodology breaks down. The best estimate of P{competition=0 given network=1} is 1, but do you really believe that if you have 217 million observations not a single value of competition=1 and network=1 will occur? Let's look at the following example.
I start by reproducing your data for network and competition (which I shorten to net and comp), and create a third binary variable z.
Now let's look at what happens when we try to model comp as a function of net and z.Code:. summarize Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- net | 217 .0967742 .2963336 0 1 comp | 217 .1290323 .3360108 0 1 z | 217 .4976959 .5011507 0 1 . tab comp net | net comp | 0 1 | Total -----------+----------------------+---------- 0 | 168 21 | 189 1 | 28 0 | 28 -----------+----------------------+---------- Total | 196 21 | 217
In your data, every observation with net != 0 has the dependent variable comp == 0, and that is what logit tells us in the note at the top of it's output. It cannot deal with that, so it drops the variable net and the 21 observations for which net != 0. The objective of this is to show you that the problem you are experiencing is not unique to polychoric and tetrachoric.Code:. logit comp net z note: net != 0 predicts failure perfectly net dropped and 21 obs not used Iteration 0: log likelihood = -80.382798 Iteration 1: log likelihood = -78.760538 Iteration 2: log likelihood = -78.731712 Iteration 3: log likelihood = -78.731702 Iteration 4: log likelihood = -78.731702 Logistic regression Number of obs = 196 LR chi2(1) = 3.30 Prob > chi2 = 0.0692 Log likelihood = -78.731702 Pseudo R2 = 0.0205 ------------------------------------------------------------------------------ comp | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- net | 0 (omitted) z | .7548408 .4237117 1.78 0.075 -.0756188 1.5853 _cons | -2.208275 .3331501 -6.63 0.000 -2.861237 -1.555312 ------------------------------------------------------------------------------
Now let's look at tetrachoric.
Same sort of results you got - tetrachoric tells us the correlation matrix is not positive semidefinite, that adjusting it to be positive seimidefinite would result in changing correlations by no more than 0.0661, and shows us the correlation matrix, in which the correlation between net and comp is shown as -1.0. For later reference, I capture and display the three eigenvalues, and we indeed see that the smallest is negative. And then pcmat declines to perform.Code:. tetrachoric comp net z (obs=217) matrix with tetrachoric correlations is not positive semidefinite; it has 1 negative eigenvalue maxdiff(corr,adj-corr) = 0.0661 (adj-corr: tetrachoric correlations adjusted to be positive semidefinite) | comp net z -------------+--------------------------- comp | 1.0000 net | -1.0000 1.0000 z | 0.2235 0.1723 1.0000 . matrix r = r(Rho) . matrix symeigen e v = r . matrix list v v[1,3] e1 e2 e3 r1 2.0013614 1.0716784 -.07303978 . pcamat r, n(217) r not positive (semi)definite
Now let's try tetrachoric with the posdef option to actually do the adjusting referred to in the previous output.
We note that as advertised, when we compare the adjusted correlations to the earlier unadjusted correlations, the largest adjustment was to the correlation between comp and net, which changed from -1.0 to -0.9339. We see that the third eigenvalue has been set to (effectively) zero, the first two are somewhat different, and that pcamat uses the adjusted correlation matrix to produce two principal components that account for 100% of the variance.Code:. tetrachoric comp net z, posdef (obs=217) matrix with tetrachoric correlations is not positive semidefinite; it has 1 negative eigenvalue maxdiff(corr,adj-corr) = 0.0661 (adj-corr: tetrachoric correlations adjusted to be positive semidefinite) adj-corr | comp net z -------------+--------------------------- comp | 1.0000 net | -0.9339 1.0000 z | 0.2068 0.1567 1.0000 . matrix r = r(Rho) . matrix symeigen e v = r . matrix list v v[1,3] e1 e2 e3 r1 1.9352714 1.0647286 -6.661e-16 . pcamat r, n(217) Principal components/correlation Number of obs = 217 Number of comp. = 2 Trace = 3 Rotation: (unrotated = principal) Rho = 1.0000 -------------------------------------------------------------------------- Component | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Comp1 | 1.93527 .870543 0.6451 0.6451 Comp2 | 1.06473 1.06473 0.3549 1.0000 Comp3 | 0 . 0.0000 1.0000 -------------------------------------------------------------------------- Principal components (eigenvectors) ------------------------------------------------ Variable | Comp1 Comp2 | Unexplained -------------+--------------------+------------- comp | 0.7104 0.1483 | 0 net | -0.7027 0.2040 | 0 z | 0.0393 0.9677 | 0 ------------------------------------------------
Not reported here, i also tried tetrachoric with the zeroadjust option. It succeeded in producing a positive semidefinite correlation matrix and pcmat produced three principle components. I don't encourage this approach: fiddling with the data is a somewhat older approach with little theoretical justification; and I like the fact that tetrachoric, posdef reduces the number of principle components, which feels a lot like logit dropping the variable.
Finally, for completeness, polychoric.
I note that polychoric reports a missing correlation between net and comp, rather than -1.0 as in tetrachoric. It provides no options for accommodating the problem data, and pcmat is of course unable to extract principle components. My own feeling on this is that tetrachoric reporting -1.0 correlation is appropriate - after all, whenever one of the variables is 1 the other is zero. Perhaps an expert would feel otherwise.Code:. polychoric comp net z could not calculate numerical derivatives missing values encountered could not calculate numerical derivatives missing values encountered Polychoric correlation matrix comp net z comp 1 net . 1 z .22407535 .17295066 1 . matrix r = r(R) . matrix list r symmetric r[3,3] comp net z comp 1 net . 1 z .22407535 .17295066 1 . pcamat r, n(217) matrix r has missing valuesComment
Comment