Dear all,

I am trying to determine the number of groups or classes for a latent variable using seven observed variables. I am using Stata 15.1.

I followed example 52g of the Stata manual (Latent profile model), on the section "comparing models", which tells us to look for the smallest AIC and BIC values.

My results produced two low(er) BIC values, in the five class model, and then in the seven class model. This is confusing as I was expecting to obtain a single low value and then go with it. My understanding is that the best solution is five classes. Another source of confusion is that a previous model I estimated using Hierarchical clustering signals the solution is three classes, which is consistent with the literature.

Maybe some of you have insights on this topic? Many thanks.

My code looks as follows:

Code:
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 2)
estimates store twoclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 3)
estimates store threeclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 4)
estimates store fourclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 5)
estimates store fiveclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 6)
estimates store sixclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 7)
estimates store sevenclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 8)
estimates store eightclass
gsem (norms trust farming lfunction informal engagement advisory <- ), lclass(C 9)
estimates store nineclass
estimates stats twoclass threeclass fourclass fiveclass sixclass sevenclass eightclass nineclass
My data look like this:

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input float(norms trust farming lfunction informal engagement advisory)
       .        .        .        .        .        .        .
 -.98162   -.3114  -.42686   .27697  -.58359   -.9699  -.01755
-1.27795   .07518  -.92345  -.60814  -.41226 -1.04472  -.03326
 -.17439   .06842  -.21618  1.90339   .05599  -.46079   .11537
  .00181   .34967  1.73676  1.62089  1.70806   .55895   .95268
-1.07155  -.67026   .18111   .09381  -.60163  -.01348  1.24672
 -.65683  -.01478  -.42252   .14127   .32071  -.36836  -.41697
 -.62188  1.07709    .2193  1.59195  -.77941    .1342  -.82457
       .        .        .        .        .        .        .
 -.19673  -.27395  2.01558  1.58268  1.15111  2.04795   .87557
       .        .        .        .        .        .        .
       .        .        .        .        .        .        .
 -.23446  -.31216   .38219  -.76928   .67551   .34163   .66063
  .66597   .02493    .7812  -.55981  -.53341   .14777  -.02744
  .79905   .67628   1.2509   .20092  1.06249    .7914  -.32487
  .57796  1.00764  -.01036  -.49744   .72682   .09987  -.28355
 -2.1567 -2.00231  -.75437  -.58971 -1.35053  -.96453    -.322
  .28847   .48866  1.78863  1.77702   .28262  -.49722  -.70806
   2.917   2.1843  1.47226   .17037  1.46298  2.07718  -.79311
 -.42906   .01127  -.33037  -.76792   -.3787  1.01925   .38168
-1.28062  -.90478  -.84523  -.70117  -.86212   -.9561  -.07887
 -.15234  -.11308  -.42957  -.55775 -1.05749   .16358  -.07475
  .01219   .27228  -.82642  -.89828  -.62624   .08204   .52512
 -.24257  -.09245  -.19699   .06336  -.42748   -.1867  -.03323
       .        .        .        .        .        .        .
 -.25378   .19178  -.55938  -.83342  -.29252    .0079  1.39661
 -.34622  -.23197  -.50193   .01962  -.77826  -.07785  -.54594
-1.33258 -2.12957  -.60777    .1453  -.85057  -.37469   .15513
 -.49857  -.32841   .08047  -.85962   .55352   .11355   .83447
       .        .        .        .        .        .        .
  .00208  -.25685   .15314  -.80633   .78764   .58573    -.569
 2.44616  1.93312   .43792   .16945   .05415  -.12629  -.81038
-1.16391  -.91032 -1.41753   -.1193  -.59082  -.48461    .4458
       .        .        .        .        .        .        .
 -.63856 -1.29752  -.74769   .63711  -.58303   .14735  1.02066
  .80684  1.43026  -.11052  1.79622  -.49766  -.46734   .25756
 -.89285   -.2508  -.75942  -.76664  -.94423  -.70646  -.33857
  .55308   .30491   .00904  -.71084   .95948  1.22393    .2342
       .        .        .        .        .        .        .
       .        .        .        .        .        .        .
  .82427   .15126  1.18409  1.81541   .52152  1.28638  -.50343
-1.06096  -.24109  -.44379  -.69832   .67544   -.5215   .93901
  .32824  -.22754  -.63507  1.54957   .64834   .78442   .10655
  .11212   .36787   .57904  1.75799  -.92055  -.42177  -.80624
 -.01378  -.18003  -.18454  -.85153  -.18396  -.31322  -.77143
 1.10172  1.12238   .04267   .83061   .18984   .64337  -.48618
   .0956  -.64086  -.32717   .65141   -.5537   .44379  -.63879
 -.03716   .97456  -.93637  1.40202   .79696   -.2963    .1341
 -.11278   .63474   .30942  1.67336  -.72935  -.66114  -.24077
  .32976   .95995    .0936  1.41741   .19751   .41717  -.25109
  .28598   .94149  -.49551  -.70068    .0374  -.95552  -.62067
 -.43843  -.04589   .29333  1.56714    .7755  -.53211   .97443
  .90736   .57099   .12578   .68461   .42543   .55269   .03414
 1.19604  1.12332  -.48926  -.74625   .88298  -.30151   .43248
       .        .        .        .        .        .        .
 -.58343   .48143  -.38741  -.52045  -.01152  -.45304  -.62327
  .57667   .89587  -.80499   -.6647  -.71928  -.12715  -.01692
  .03393  -.24292   .03263   .11358  -.42574   .28757  -.38657
 -.24131  -.09174   -.2946  -.46846  -.82168  -.35623   .15242
       .        .        .        .        .        .        .
   .1217   .69624   .78358  -.82037   1.5453   .41513 -1.07919
  .67261   -.6634  -.66666  -.82749   -.4517    -.182  -.56629
   .0297   .76154  -.69922   .98276   .15046  -.87889  -.37813
       .        .        .        .        .        .        .
 1.14868  -.21988  -.63483 -1.00056    .1877   .75215   .87147
 -.00828   .06452   .10774  -.54093  -.26943  -.15246  -.82105
  .90453  -.36292   .81872   .08099  1.17278   .42526    .0197
-1.24279   -.8721  -.92597  -.79885   .48879  -.54551   .46449
 -.79878    .0201   .08659    .0727   .55572  1.20979  -.15132
  .57728   .60675   .25095   .18553   .04941   .37787   .28629
 1.16343  1.63819   .81735   .08798   .22632  1.45681   .50109
 -.25402   .32468  -.69245  -.77693  -.35289   .28376   -.3427
 -.45147   .11576  -.32327  -.68546   .36101  -.15307  -.44881
 -.04494  -.06861   .13233  -.90248   .06439   .68085  -.84557
       .        .        .        .        .        .        .
  -.1818   .37248   -.4322   .55371   .64133    .4286  -.27781
   1.214  2.02057  1.22313   .09709  -.30147  -.15322 -1.23281
 -.30937   .13472   .37401  -.67369  1.07601  -.01124   -.6008
  .26423   .02267  -.90632  -.94903  -.59597   .25893   -.1776
       .        .        .        .        .        .        .
 1.07253   .92323   .88192  1.54814  1.86285  1.49033  -.60765
  .23948   .95284   .20922  -.53522  -.98768  -.58779  -.82547
  .21964  -.21275   .37773  1.64471  1.00786   .57222  -.71256
 -.76473  -.32201  -.40709  1.66059  -.61379  -.23045    .0912
  .18023  -.45177  -.81183    -.848   .86402  -.17908  1.68735
-1.49997 -1.19828 -1.28282  -.81151  -.76796   -.6276   .50403
  .30224  -.10522   .01976  -.64449  -.02935   .41612   .31947
       .        .        .        .        .        .        .
 -.52266 -1.34936  -.73154  -.76804  -.31962  -.05722   .41141
 -.96957  -.78634   .53871   .12362  -.29297  -.09075   .11078
 -.78604  -.11771  -.84394  -.80837  -.77715   -.6895  -.24794
  .30094  -.48776  -.39064  -.83408   .62239  1.70087  -.06108
 -.72275  -.19341   .51569   .30624  -.70441  -.29125   .93915
  .20981  -.05193   .47408  -.85325   .38379   .86116  -.68158
 -.35538   .03694  -.86964  -.83604  -.72419  -.46129   .42457
 -.19418   .13862   .89344  1.42595  1.37781  1.08988    .0639
 -.01774  -.21469  -.08852  -.67479  -.96608   .11353  -.91709
       .        .        .        .        .        .        .
       .        .        .        .        .        .        .
  .58376  1.12999   .99077   .02522   .03026  -.32304 -1.24935
end
My model comparison looks as follows:

Code:
Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |        Obs  ll(null)  ll(model)      df         AIC        BIC
-------------+---------------------------------------------------------------
    twoclass |        398         .  -2956.341      22    5956.682   6044.384
  threeclass |        398         .  -2872.062      30    5804.124   5923.718
   fourclass |        398         .  -2843.916      38    5763.832   5915.317
   fiveclass |        398         .  -2811.454      46    5714.908   5898.285
    sixclass |        398         .  -2800.841      54    5709.683   5924.951
  sevenclass |        398         .  -2737.597      62    5599.194   5846.354
  eightclass |        398         .  -2724.188      70    5588.376   5867.427
   nineclass |        398         .  -2712.336      78    5580.671   5891.614
-----------------------------------------------------------------------------
               Note: N=Obs used in calculating BIC; see [R] BIC note.