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  • Interpret interaction term of two continuous variables after ordered logit estimation.

    Hi Statalist members,

    I'm running the ordered logit model and find struggling how to interpret the results of an interaction term of two continuous variables.

    My dependent variable is debt maturity, which takes a value of 1 if a firm use long term debt, 2 if a firm only uses short term debt and 3 if a firm does not use any long term or short term debt in a given year. Although I know this order is quite ambiguous to Stata experts here ( and most of you will recommend me to use the multinomial logit, which seems not work with my dataset), please ignore that issue in this post.

    My main variable of interest is firm cash flow volatility (CFV)

    My model is Debt maturity = alpha + beta_1 * CFV + beta_2 * other firm-level control variables + beta_3 * country-level variables + error term

    Now I would like to test if a country's banking system strengthen or weaken the influence of cash flow volatility on debt maturity.

    The additional mode is alpha + beta_1 * CFV + beta_2 * other firm-level control variables + beta_3 * country-level variables + beta_4* bank*CFV) + error term

    I searched and found a few useful posts in this forum, suggesting I should use the margin command to figure out the effect of an interaction term and I can't interpret the coefficient of CFV as in the model without interactions any more. However, I still don't know how to interpret the results after getting the marginal effect of CFV and interaction.

    Here are the cash flow volatility marginal effects ( on three categories of debt maturity)



    Delta-method
    dy/dx Std. Err. z P>z [95% Conf. Interval]

    KS_oi_5_w01
    _predict
    1 -.0011547 .0002561 -4.51 0.000 -.0016566 -.0006528
    2 .0003506 .0000782 4.48 0.000 .0001972 .0005039
    3 .0008041 .0001782 4.51 0.000 .0004548 .0011535


    And here are the interaction of the banking system and cash flow volatility marginal effects



    Delta-method
    dy/dx Std. Err. z P>z [95% Conf. Interval]

    baKS
    _predict
    1 -5.32e-06 2.52e-06 -2.11 0.035 -.0000103 -3.70e-07
    2 1.61e-06 7.67e-07 2.10 0.035 1.10e-07 3.12e-06
    3 3.70e-06 1.76e-06 2.11 0.035 2.58e-07 7.15e-06





    Any help would appreciate.
    Regards.
    Huyen
    Huyen

  • #2
    The interpretation of the -margins- output requires seeing the actual -margins- command and also the actual regression command that was run. Please post back showing those. Also, when posting back, please put these results inside code delimiters so that they will align well and be easy to read. If you are unfamiliar with code delimiters, read Forum FAQ #12 for instructions.

    Comment


    • #3
      Hi Clyde,
      After running this regression

      Code:
       ologit DebtMat_D KS_oi_5_w01 $CONTROLSF LEV_w01 $CONTROLSC    gKS IKS lKS cKS sKS bKS baKS i.Ind49 i.fyear i.fic_n , cluster(gvkey_n)
      
      Iteration 0:   log pseudolikelihood = -140510.67  
      Iteration 1:   log pseudolikelihood = -111787.19  
      Iteration 2:   log pseudolikelihood = -103532.64  
      Iteration 3:   log pseudolikelihood = -102406.66  
      Iteration 4:   log pseudolikelihood = -102388.01  
      Iteration 5:   log pseudolikelihood = -102387.99  
      Iteration 6:   log pseudolikelihood = -102387.99  
      
      Ordered logistic regression                     Number of obs     =    206,445
                                                      Wald chi2(131)    =    8294.93
                                                      Prob > chi2       =     0.0000
      Log pseudolikelihood = -102387.99               Pseudo R2         =     0.2713
      
                                                              (Std. Err. adjusted for 25,957 clusters in gvkey_n)
      -----------------------------------------------------------------------------------------------------------
                                                |               Robust
                                      DebtMat_D |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
      ------------------------------------------+----------------------------------------------------------------
                                    KS_oi_5_w01 |  -.0051044   .0066512    -0.77   0.443    -.0181404    .0079317
                                        MB2_w01 |  -.0992163   .0073619   -13.48   0.000    -.1136454   -.0847872
                                       amat_w01 |    .010239   .0005893    17.37   0.000      .009084    .0113941
                                      fsize_w01 |  -.3156914   .0098587   -32.02   0.000    -.3350141   -.2963687
                                       abne_w01 |  -.2988906   .0464876    -6.43   0.000    -.3900046   -.2077766
                                       tang_w01 |  -.8338541   .0486571   -17.14   0.000    -.9292203   -.7384878
                                       prof_w01 |   .4932033   .0749417     6.58   0.000     .3463202    .6400863
                                     xrd_at_w01 |   .7710762   .2308709     3.34   0.001     .3185776    1.223575
                                        LEV_w01 |  -8.412556   .1946282   -43.22   0.000     -8.79402   -8.031092
                                       g_gdpcap |  -.0303184   .0053317    -5.69   0.000    -.0407683   -.0198685
                                      Inflation |   .0006956   .0004414     1.58   0.115    -.0001695    .0015606
                                    lawandorder |  -.0608424   .0325517    -1.87   0.062    -.1246426    .0029578
                                     corruption |  -.0911549   .0235591    -3.87   0.000    -.1373299   -.0449799
                                       stmktcap |  -.0041896   .0006786    -6.17   0.000    -.0055196   -.0028596
                                         prbond |   .0026667   .0012862     2.07   0.038     .0001457    .0051877
                                         dbagdp |  -.0001452   .0007433    -0.20   0.845    -.0016019    .0013116
                                            gKS |     .00079   .0002692     2.93   0.003     .0002624    .0013176
                                            IKS |   -.000024   .0000163    -1.47   0.140    -.0000559    7.91e-06
                                            lKS |   .0001447   .0012854     0.11   0.910    -.0023747    .0026641
                                            cKS |   .0022141   .0010766     2.06   0.040     .0001039    .0043242
                                            sKS |   -.000038    .000022    -1.73   0.084     -.000081    5.04e-06
                                            bKS |   .0000728   .0000304     2.39   0.017     .0000132    .0001324
                                           baKS |   .0000789   .0000256     3.08   0.002     .0000286    .0001291
                                                |
                                          Ind49 |
                                   Agriculture  |   .4857292   .2667225     1.82   0.069    -.0370374    1.008496
                                 Food Products  |   .5160233    .233053     2.21   0.027     .0592478    .9727988
                                Candy and Soda  |   1.008929   .2930888     3.44   0.001     .4344855    1.583372
                          Alchoholic Beverages  |   .7576584   .2652645     2.86   0.004     .2377495    1.277567
                              Tobacco Products  |   .8093425   .5102228     1.59   0.113    -.1906758    1.809361
                         Recreational Products  |   .6271347    .254063     2.47   0.014     .1291803    1.125089
                                 Entertainment  |   .5988315   .2398691     2.50   0.013     .1286968    1.068966
                       Printing and Publishing  |   .4119099   .2457103     1.68   0.094    -.0696734    .8934931
                                Consumer Goods  |   .6792243    .230733     2.94   0.003      .226996    1.131453
                                       Apparel  |   .7057847    .236095     2.99   0.003      .243047    1.168522
                                    Healthcare  |  -.0251735   .2617695    -0.10   0.923    -.5382324    .4878853
                             Medical Equipment  |   .3273566   .2336045     1.40   0.161    -.1304998    .7852131
                       Pharmaceutical Products  |   .2003253   .2253037     0.89   0.374    -.2412618    .6419124
                                     Chemicals  |   .4440306   .2269859     1.96   0.050    -.0008536    .8889148
                   Rubber and Plastic Products  |   .1462211   .2471769     0.59   0.554    -.3382366    .6306788
                                      Textiles  |   .7889867   .2521757     3.13   0.002     .2947314    1.283242
                        Construction Materials  |   .4962261   .2308637     2.15   0.032     .0437415    .9487107
                                  Construction  |   .4282161   .2380814     1.80   0.072     -.038415    .8948471
                             Steel Works, Etc.  |   .7884989   .2339588     3.37   0.001     .3299481     1.24705
                           Fabricated Products  |   .2439145   .2857916     0.85   0.393    -.3162269    .8040558
                                     Machinery  |    .153101   .2259915     0.68   0.498    -.2898342    .5960362
                      Electrical Equipment One  |   .3151718   .2339102     1.35   0.178    -.1432837    .7736274
                        Automobiles and Trucks  |   .5370251    .237012     2.27   0.023     .0724901     1.00156
                                      Aircraft  |   .1680736   .3254565     0.52   0.606    -.4698094    .8059566
              Shipbuilding, Railroad Equipment  |   .4884643    .370907     1.32   0.188    -.2385001    1.215429
                                       Defense  |   .9090715    .642845     1.41   0.157    -.3508816    2.169025
                               Precious Metals  |   .7472766   .2471808     3.02   0.003     .2628111    1.231742
      Non_Metallic and Industrial Metal Mining  |   .6019932   .2359334     2.55   0.011     .1395722    1.064414
                                          Coal  |  -.0675343   .2846594    -0.24   0.812    -.6254565    .4903878
                     Petroleum and Natural Gas  |   .7218694   .2330333     3.10   0.002     .2651326    1.178606
                             Personal Services  |   .3279573   .2802371     1.17   0.242    -.2212974    .8772119
                             Business Services  |   .3624913    .226377     1.60   0.109    -.0811996    .8061821
                                     Computers  |   .7374067   .2349216     3.14   0.002     .2769688    1.197845
                             Computer Software  |   .5759677   .2226751     2.59   0.010     .1395326    1.012403
                      Electrical Equipment Two  |   .5750612   .2243115     2.56   0.010     .1354188    1.014704
                   Measuring and Lab Equipment  |   .4416015   .2430662     1.82   0.069    -.0347995    .9180025
                             Business Supplies  |   .3562327   .2469833     1.44   0.149    -.1278455     .840311
                           Shipping Containers  |   .3079895   .3592121     0.86   0.391    -.3960533    1.012032
                                     Wholesale  |    .699703   .2264752     3.09   0.002     .2558198    1.143586
                                        Retail  |   .7490526   .2272588     3.30   0.001     .3036337    1.194472
                   Restaurants, Hotels, Motels  |    .285181   .2455947     1.16   0.246    -.1961758    .7665377
                                 Miscellaneous  |   .4894117   .3109789     1.57   0.116    -.1200958    1.098919
                                                |
                                          fyear |
                                          1991  |   .0588864   .0556829     1.06   0.290    -.0502501    .1680228
                                          1992  |    .231627   .0650699     3.56   0.000     .1040924    .3591617
                                          1993  |   .2937276   .0690026     4.26   0.000     .1584851    .4289702
                                          1994  |   .2453308   .0742541     3.30   0.001     .0997954    .3908662
                                          1995  |   .2421901   .0772207     3.14   0.002     .0908404    .3935398
                                          1996  |   .3943849   .0814986     4.84   0.000     .2346505    .5541192
                                          1997  |   .5072385   .0891416     5.69   0.000     .3325242    .6819528
                                          1998  |   .6699373    .094549     7.09   0.000     .4846246      .85525
                                          1999  |   .8411582    .099558     8.45   0.000      .646028    1.036288
                                          2000  |   .9496413   .1004557     9.45   0.000     .7527517    1.146531
                                          2001  |   .7063786   .0936392     7.54   0.000     .5228491     .889908
                                          2002  |   .7625764   .0908149     8.40   0.000     .5845826    .9405703
                                          2003  |    .851788   .0918052     9.28   0.000     .6718531    1.031723
                                          2004  |   .9575286   .0941927    10.17   0.000     .7729143    1.142143
                                          2005  |    .974517    .095634    10.19   0.000     .7870779    1.161956
                                          2006  |   .9186351   .1016431     9.04   0.000     .7194182    1.117852
                                          2007  |   .9380663   .1086177     8.64   0.000     .7251796    1.150953
                                          2008  |   1.076019   .1021339    10.54   0.000     .8758399    1.276197
                                          2009  |   .8439808   .0995122     8.48   0.000     .6489406    1.039021
                                          2010  |   1.061516   .1038334    10.22   0.000     .8580067    1.265026
                                          2011  |   1.132838   .0991288    11.43   0.000     .9385495    1.327127
                                          2012  |   .9838675   .1013854     9.70   0.000     .7851558    1.182579
                                          2013  |   .9454784   .1024842     9.23   0.000     .7446131    1.146344
                                          2014  |   .7689163     .10498     7.32   0.000     .5631593    .9746732
                                          2015  |   .7760459   .1107892     7.00   0.000     .5589031    .9931886
                                                |
                                          fic_n |
                                           AUT  |  -.6079288   .2918801    -2.08   0.037    -1.180003   -.0358543
                                           BEL  |  -1.667304   .4083994    -4.08   0.000    -2.467753   -.8668563
                                           BRA  |  -.9096214   .2565029    -3.55   0.000    -1.412358    -.406885
                                           CAN  |   .2949448   .1606213     1.84   0.066    -.0198671    .6097567
                                           CHE  |    .165217   .1952645     0.85   0.397    -.2174944    .5479284
                                           CHL  |  -1.389983   .3130999    -4.44   0.000    -2.003648   -.7763186
                                           CHN  |     .65946    .125549     5.25   0.000     .4133886    .9055315
                                           COL  |  -.8436307   .5057719    -1.67   0.095    -1.834925     .147664
                                           CYP  |   -1.01551   .6155928    -1.65   0.099    -2.222049    .1910299
                                           DEU  |   -.561597   .1244371    -4.51   0.000    -.8054893   -.3177048
                                           DNK  |  -1.270424   .2768506    -4.59   0.000    -1.813041   -.7278064
                                           ESP  |  -2.420024   .4803101    -5.04   0.000    -3.361415   -1.478634
                                           FIN  |  -1.236761   .3632286    -3.40   0.001    -1.948676   -.5248458
                                           FRA  |   -1.81651   .1415741   -12.83   0.000     -2.09399    -1.53903
                                           GBR  |   .0425344   .0949387     0.45   0.654    -.1435421    .2286109
                                           GRC  |   .2545578   .1853557     1.37   0.170    -.1087326    .6178483
                                           HKG  |   1.281198   .3564844     3.59   0.000     .5825011    1.979894
                                           HRV  |  -.6106547   .4365877    -1.40   0.162    -1.466351    .2450415
                                           HUN  |  -.6726321   .4989701    -1.35   0.178    -1.650595    .3053313
                                           IDN  |   -.172668   .2100659    -0.82   0.411    -.5843896    .2390536
                                           IND  |  -.4785529   .1539713    -3.11   0.002     -.780331   -.1767748
                                           IRL  |  -.4171294   .4022063    -1.04   0.300    -1.205439    .3711804
                                           ISR  |  -.0977618     .16477    -0.59   0.553    -.4207051    .2251815
                                           ITA  |  -1.642778   .3123849    -5.26   0.000    -2.255041   -1.030515
                                           JPN  |    .018633   .0890212     0.21   0.834    -.1558454    .1931114
                                           KOR  |   .3284718   .1042979     3.15   0.002     .1240516     .532892
                                           MEX  |   .1529733    .269077     0.57   0.570    -.3744079    .6803546
                                           MYS  |      -.279    .127866    -2.18   0.029    -.5296128   -.0283873
                                           NLD  |  -.2223243   .2133118    -1.04   0.297    -.6404077    .1957591
                                           NOR  |  -.3958815   .2054656    -1.93   0.054    -.7985866    .0068235
                                           PER  |  -.0811313   .2979033    -0.27   0.785    -.6650111    .5027485
                                           PHL  |   .2002238   .2320077     0.86   0.388    -.2545029    .6549505
                                           POL  |  -1.529306   .1881649    -8.13   0.000    -1.898103    -1.16051
                                           PRT  |   1.100433   .7161248     1.54   0.124    -.3031459    2.504012
                                           RUS  |  -.2372758   .2958271    -0.80   0.423    -.8170862    .3425346
                                           SGP  |   .3088691   .1376343     2.24   0.025     .0391109    .5786273
                                           SWE  |   -.179954   .1259272    -1.43   0.153    -.4267668    .0668589
                                           THA  |   .0656707   .1621462     0.41   0.685      -.25213    .3834714
                                           TUR  |   .1925098   .1822309     1.06   0.291    -.1646561    .5496758
                                           USA  |  -.0121991   .0978045    -0.12   0.901    -.2038924    .1794941
                                           ZAF  |  -.3959545   .2108142    -1.88   0.060    -.8091428    .0172338
      ------------------------------------------+----------------------------------------------------------------
                                          /cut1 |  -1.520699   .3461273                     -2.199096   -.8423024
                                          /cut2 |  -.4371754    .346579                     -1.116458    .2421069
      -----------------------------------------------------------------------------------------------------------
      I only found the coefficient associated with baKS, which is the interaction term of a country's banking system with cash flow volatility (KS_oi_5_w01) significant, then I run another regression to interpret this coefficient

      ( The post exceeds the word limits so I have to post two replies)

      Comment


      • #4
        Code:
        ologit DebtMat_D KS_oi_5_w01 $CONTROLSF LEV_w01 $CONTROLSC  baKS i.Ind49 i.fyear i.fic_n , cluster(gvkey_n)
        
        Iteration 0:   log pseudolikelihood = -140510.67  
        Iteration 1:   log pseudolikelihood = -111791.83  
        Iteration 2:   log pseudolikelihood = -103517.52  
        Iteration 3:   log pseudolikelihood = -102426.18  
        Iteration 4:   log pseudolikelihood = -102407.82  
        Iteration 5:   log pseudolikelihood = -102407.79  
        Iteration 6:   log pseudolikelihood = -102407.79  
        
        Ordered logistic regression                     Number of obs     =    206,445
                                                        Wald chi2(125)    =    8202.10
                                                        Prob > chi2       =     0.0000
        Log pseudolikelihood = -102407.79               Pseudo R2         =     0.2712
        
                                                                (Std. Err. adjusted for 25,957 clusters in gvkey_n)
        -----------------------------------------------------------------------------------------------------------
                                                  |               Robust
                                        DebtMat_D |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
        ------------------------------------------+----------------------------------------------------------------
                                      KS_oi_5_w01 |   .0100127   .0022209     4.51   0.000     .0056598    .0143655
                                          MB2_w01 |  -.0987846    .007334   -13.47   0.000     -.113159   -.0844102
                                         amat_w01 |   .0102334   .0005902    17.34   0.000     .0090767    .0113901
                                        fsize_w01 |  -.3155809   .0098544   -32.02   0.000    -.3348952   -.2962665
                                         abne_w01 |   -.297045   .0461889    -6.43   0.000    -.3875736   -.2065163
                                         tang_w01 |   -.838332   .0486385   -17.24   0.000    -.9336617   -.7430022
                                         prof_w01 |   .4818726   .0739659     6.51   0.000     .3369021    .6268431
                                       xrd_at_w01 |   .7971725   .2296823     3.47   0.001     .3470035    1.247341
                                          LEV_w01 |  -8.410532      .1946   -43.22   0.000    -8.791941   -8.029123
                                         g_gdpcap |  -.0231236   .0048162    -4.80   0.000    -.0325632   -.0136841
                                        Inflation |   .0001327   .0002965     0.45   0.654    -.0004484    .0007138
                                      lawandorder |  -.0613917   .0307742    -1.99   0.046     -.121708   -.0010754
                                       corruption |  -.0765255   .0219898    -3.48   0.001    -.1196248   -.0334262
                                         stmktcap |  -.0044963   .0006394    -7.03   0.000    -.0057495   -.0032432
                                           prbond |   .0034049   .0012427     2.74   0.006     .0009693    .0058405
                                           dbagdp |   .0001205   .0007238     0.17   0.868    -.0012981    .0015392
                                             baKS |   .0000461   .0000219     2.11   0.035     3.22e-06     .000089
                                                  |
                                            Ind49 |
                                     Agriculture  |   .4941466   .2673099     1.85   0.065    -.0297711    1.018064
                                   Food Products  |   .5249754    .233292     2.25   0.024     .0677316    .9822193
                                  Candy and Soda  |   1.018373   .2931176     3.47   0.001     .4438727    1.592873
                            Alchoholic Beverages  |   .7657073    .265569     2.88   0.004     .2452015    1.286213
                                Tobacco Products  |   .8149379   .5103465     1.60   0.110     -.185323    1.815199
                           Recreational Products  |   .6318073   .2544344     2.48   0.013     .1331251     1.13049
                                   Entertainment  |    .603786   .2402789     2.51   0.012     .1328481    1.074724
                         Printing and Publishing  |   .4176964   .2461339     1.70   0.090    -.0647172    .9001101
                                  Consumer Goods  |   .6839537    .231024     2.96   0.003      .231155    1.136752
                                         Apparel  |   .7099385   .2364263     3.00   0.003     .2465514    1.173326
                                      Healthcare  |  -.0163825   .2619527    -0.06   0.950    -.5298003    .4970352
                               Medical Equipment  |   .3302004   .2339432     1.41   0.158    -.1283198    .7887207
                         Pharmaceutical Products  |   .2109182   .2254983     0.94   0.350    -.2310504    .6528868
                                       Chemicals  |   .4494764   .2273176     1.98   0.048     .0039421    .8950107
                     Rubber and Plastic Products  |   .1563614   .2474626     0.63   0.527    -.3286563    .6413791
                                        Textiles  |   .7984527   .2524835     3.16   0.002     .3035942    1.293311
                          Construction Materials  |   .5034542   .2311519     2.18   0.029     .0504048    .9565037
                                    Construction  |   .4336916   .2384028     1.82   0.069    -.0335693    .9009525
                               Steel Works, Etc.  |   .7953972   .2342594     3.40   0.001     .3362572    1.254537
                             Fabricated Products  |   .2460185   .2863962     0.86   0.390    -.3153077    .8073447
                                       Machinery  |   .1575207   .2263105     0.70   0.486    -.2860398    .6010812
                        Electrical Equipment One  |   .3201829   .2342249     1.37   0.172    -.1388895    .7792554
                          Automobiles and Trucks  |   .5433898   .2373046     2.29   0.022     .0782813    1.008498
                                        Aircraft  |   .1748933   .3257299     0.54   0.591    -.4635256    .8133122
                Shipbuilding, Railroad Equipment  |   .4984448   .3711194     1.34   0.179    -.2289359    1.225826
                                         Defense  |   .9110807   .6432799     1.42   0.157    -.3497247    2.171886
                                 Precious Metals  |   .7551503   .2473642     3.05   0.002     .2703254    1.239975
        Non_Metallic and Industrial Metal Mining  |   .6052895   .2361843     2.56   0.010     .1423768    1.068202
                                            Coal  |  -.0746437   .2852365    -0.26   0.794     -.633697    .4844096
                       Petroleum and Natural Gas  |   .7276036   .2333674     3.12   0.002     .2702118    1.184995
                               Personal Services  |   .3326592   .2804095     1.19   0.235    -.2169333    .8822517
                               Business Services  |   .3680587    .226705     1.62   0.104    -.0762749    .8123923
                                       Computers  |   .7424846   .2352304     3.16   0.002     .2814416    1.203528
                               Computer Software  |   .5784136   .2230003     2.59   0.009      .141341    1.015486
                        Electrical Equipment Two  |   .5789206   .2246373     2.58   0.010     .1386396    1.019202
                     Measuring and Lab Equipment  |   .4451445   .2433709     1.83   0.067    -.0318536    .9221426
                               Business Supplies  |   .3664276    .247165     1.48   0.138    -.1180069    .8508622
                             Shipping Containers  |   .3193641   .3588074     0.89   0.373    -.3838855    1.022614
                                       Wholesale  |   .7041549   .2267843     3.10   0.002     .2596657    1.148644
                                          Retail  |   .7566017   .2275703     3.32   0.001      .310572    1.202631
                     Restaurants, Hotels, Motels  |   .2948672   .2458327     1.20   0.230     -.186956    .7766905
                                   Miscellaneous  |   .4948622   .3111194     1.59   0.112    -.1149206    1.104645
                                                  |
                                            fyear |
                                            1991  |   .0478538   .0553452     0.86   0.387    -.0606209    .1563284
                                            1992  |   .2314154   .0645841     3.58   0.000     .1048329    .3579979
                                            1993  |   .2884336   .0684913     4.21   0.000     .1541931     .422674
                                            1994  |   .2485886   .0736259     3.38   0.001     .1042845    .3928927
                                            1995  |   .2402825   .0767248     3.13   0.002     .0899046    .3906604
                                            1996  |    .389684   .0808584     4.82   0.000     .2312044    .5481636
                                            1997  |   .4868546   .0882609     5.52   0.000     .3138664    .6598428
                                            1998  |   .6492823   .0937267     6.93   0.000     .4655814    .8329832
                                            1999  |   .8178225   .0985749     8.30   0.000     .6246191    1.011026
                                            2000  |   .9246871   .0994937     9.29   0.000     .7296831    1.119691
                                            2001  |    .679545   .0926606     7.33   0.000     .4979336    .8611565
                                            2002  |   .7378798   .0897632     8.22   0.000     .5619472    .9138123
                                            2003  |   .8286484   .0906864     9.14   0.000     .6509062    1.006391
                                            2004  |   .9388822   .0931766    10.08   0.000     .7562593    1.121505
                                            2005  |   .9550393   .0946732    10.09   0.000     .7694833    1.140595
                                            2006  |   .8926401   .1006127     8.87   0.000     .6954428    1.089837
                                            2007  |   .9118378   .1076076     8.47   0.000     .7009307    1.122745
                                            2008  |   1.053451   .1012435    10.41   0.000     .8550172    1.251885
                                            2009  |   .8199462   .0985915     8.32   0.000     .6267105    1.013182
                                            2010  |   1.037379   .1029246    10.08   0.000     .8356502    1.239107
                                            2011  |   1.111155   .0982362    11.31   0.000     .9186153    1.303694
                                            2012  |   .9618468   .1005202     9.57   0.000     .7648308    1.158863
                                            2013  |   .9214399   .1016192     9.07   0.000       .72227     1.12061
                                            2014  |   .7480806   .1041488     7.18   0.000     .5439526    .9522086
                                            2015  |   .7575959    .109936     6.89   0.000     .5421253    .9730666
                                                  |
                                            fic_n |
                                             AUT  |  -.6126646   .2900246    -2.11   0.035    -1.181102   -.0442268
                                             BEL  |  -1.685696   .4077713    -4.13   0.000    -2.484913   -.8864793
                                             BRA  |  -.9469862   .2560525    -3.70   0.000     -1.44884   -.4451325
                                             CAN  |   .2812779   .1605531     1.75   0.080    -.0334003    .5959561
                                             CHE  |   .1463367   .1948234     0.75   0.453    -.2355101    .5281835
                                             CHL  |  -1.409904   .3141855    -4.49   0.000    -2.025696   -.7941114
                                             CHN  |   .6308343   .1248283     5.05   0.000     .3861752    .8754933
                                             COL  |  -.8460806   .5064874    -1.67   0.095    -1.838778    .1466166
                                             CYP  |  -1.017508   .6213726    -1.64   0.102    -2.235376    .2003598
                                             DEU  |  -.5578331   .1239633    -4.50   0.000    -.8007968   -.3148695
                                             DNK  |  -1.218518   .2635688    -4.62   0.000    -1.735103   -.7019322
                                             ESP  |  -2.435722   .4800787    -5.07   0.000    -3.376659   -1.494785
                                             FIN  |  -1.238112   .3629535    -3.41   0.001    -1.949488   -.5267367
                                             FRA  |  -1.835735   .1415487   -12.97   0.000    -2.113165   -1.558305
                                             GBR  |   .0204194   .0948368     0.22   0.830    -.1654573    .2062961
                                             GRC  |    .242073   .1862281     1.30   0.194    -.1229274    .6070733
                                             HKG  |    1.26579   .3591318     3.52   0.000     .5619041    1.969675
                                             HRV  |  -.5900594   .4385059    -1.35   0.178    -1.449515    .2693963
                                             HUN  |  -.6667466   .4967467    -1.34   0.180    -1.640352     .306859
                                             IDN  |   -.198277   .2094094    -0.95   0.344     -.608712    .2121579
                                             IND  |  -.4956916    .153169    -3.24   0.001    -.7958973   -.1954858
                                             IRL  |  -.4325902   .3991141    -1.08   0.278    -1.214839     .349659
                                             ISR  |  -.1340825   .1638583    -0.82   0.413    -.4552388    .1870739
                                             ITA  |  -1.652573   .3132525    -5.28   0.000    -2.266537    -1.03861
                                             JPN  |  -.0062688   .0881769    -0.07   0.943    -.1790923    .1665548
                                             KOR  |   .3059268   .1038743     2.95   0.003     .1023369    .5095166
                                             MEX  |   .1573826   .2688252     0.59   0.558    -.3695052    .6842704
                                             MYS  |  -.3004064   .1277227    -2.35   0.019    -.5507382   -.0500746
                                             NLD  |  -.2326297   .2123913    -1.10   0.273    -.6489091    .1836496
                                             NOR  |  -.3996846   .2046473    -1.95   0.051    -.8007859    .0014167
                                             PER  |  -.1124155   .2952695    -0.38   0.703     -.691133     .466302
                                             PHL  |   .1863668   .2326802     0.80   0.423     -.269678    .6424116
                                             POL  |  -1.549461   .1876713    -8.26   0.000     -1.91729   -1.181632
                                             PRT  |     1.0819   .7159941     1.51   0.131    -.3214222    2.485223
                                             RUS  |  -.2955311   .2965418    -1.00   0.319    -.8767422    .2856801
                                             SGP  |   .2875965   .1380747     2.08   0.037     .0169751    .5582179
                                             SWE  |  -.1906895    .125562    -1.52   0.129    -.4367865    .0554075
                                             THA  |   .0479262   .1623427     0.30   0.768    -.2702597    .3661121
                                             TUR  |   .1805885   .1815414     0.99   0.320    -.1752261    .5364031
                                             USA  |   -.032005   .0971921    -0.33   0.742    -.2224979     .158488
                                             ZAF  |  -.4356978   .2107157    -2.07   0.039     -.848693   -.0227026
        ------------------------------------------+----------------------------------------------------------------
                                            /cut1 |  -1.445463   .3438674                     -2.119431   -.7714953
                                            /cut2 |  -.3622056   .3442741                     -1.036971    .3125593
        -----------------------------------------------------------------------------------------------------------
        Then I run the margins command to calculate the marginal effects of cash flow volatility and its interaction with a country's banking system
        Code:
         margins, dydx(KS_oi_5_w01)
        
        Average marginal effects                        Number of obs     =    206,445
        Model VCE    : Robust
        
        dy/dx w.r.t. : KS_oi_5_w01
        1._predict   : Pr(DebtMat_D==1), predict(pr outcome(1))
        2._predict   : Pr(DebtMat_D==2), predict(pr outcome(2))
        3._predict   : Pr(DebtMat_D==3), predict(pr outcome(3))
        
        ------------------------------------------------------------------------------
                     |            Delta-method
                     |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
        -------------+----------------------------------------------------------------
        KS_oi_5_w01  |
            _predict |
                  1  |  -.0011547   .0002561    -4.51   0.000    -.0016566   -.0006528
                  2  |   .0003506   .0000782     4.48   0.000     .0001972    .0005039
                  3  |   .0008041   .0001782     4.51   0.000     .0004548    .0011535
        ------------------------------------------------------------------------------
        and
        Code:
         margins, dydx(baKS)
        
        Average marginal effects                        Number of obs     =    206,445
        Model VCE    : Robust
        
        dy/dx w.r.t. : baKS
        1._predict   : Pr(DebtMat_D==1), predict(pr outcome(1))
        2._predict   : Pr(DebtMat_D==2), predict(pr outcome(2))
        3._predict   : Pr(DebtMat_D==3), predict(pr outcome(3))
        
        ------------------------------------------------------------------------------
                     |            Delta-method
                     |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
        -------------+----------------------------------------------------------------
        baKS         |
            _predict |
                  1  |  -5.32e-06   2.52e-06    -2.11   0.035    -.0000103   -3.70e-07
                  2  |   1.61e-06   7.67e-07     2.10   0.035     1.10e-07    3.12e-06
                  3  |   3.70e-06   1.76e-06     2.11   0.035     2.58e-07    7.15e-06
        ------------------------------------------------------------------------------
        I would like your help to read these resutls.

        Regards,
        Huyen

        Comment


        • #5
          Well, this looks workable. But I'm confused. The title of your post refers to an interaction between two continuous variables. But your model does not contain any interaction variables at all. If you have hand calculated interaction variables by multiplying, you have wasted your efforts here: Stata will not know that they represent an interaction, and the -margins- calculations will be incorrect.

          If your title was wrong, post back and I'll proceed with interpreting the results you show in #3. If the title was right, there is no point interpreting these results as they are incorrect. In that case, you need to redo the regression and margins using factor variable notation. See -help fvvarlist-.

          Comment


          • #6
            Hi Clyde,

            Sorry, I've got your idea and re-run the regression as below
            Code:
             ologit DebtMat_D KS_oi_5_w01 $CONTROLSF LEV_w01 $CONTROLSC  c.dbagdp#c.KS_oi_5_w01 i.Ind49 i.fyear i.fic_n , cluster(gvkey_n)
            
            Iteration 0:   log pseudolikelihood = -140510.67  
            Iteration 1:   log pseudolikelihood = -111791.83  
            Iteration 2:   log pseudolikelihood = -103517.52  
            Iteration 3:   log pseudolikelihood = -102426.18  
            Iteration 4:   log pseudolikelihood = -102407.82  
            Iteration 5:   log pseudolikelihood = -102407.79  
            Iteration 6:   log pseudolikelihood = -102407.79  
            
            Ordered logistic regression                     Number of obs     =    206,445
                                                            Wald chi2(125)    =    8202.10
                                                            Prob > chi2       =     0.0000
            Log pseudolikelihood = -102407.79               Pseudo R2         =     0.2712
            
                                                                    (Std. Err. adjusted for 25,957 clusters in gvkey_n)
            -----------------------------------------------------------------------------------------------------------
                                                      |               Robust
                                            DebtMat_D |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
            ------------------------------------------+----------------------------------------------------------------
                                          KS_oi_5_w01 |   .0100127   .0022209     4.51   0.000     .0056598    .0143655
                                              MB2_w01 |  -.0987846    .007334   -13.47   0.000     -.113159   -.0844102
                                             amat_w01 |   .0102334   .0005902    17.34   0.000     .0090767    .0113901
                                            fsize_w01 |  -.3155809   .0098544   -32.02   0.000    -.3348952   -.2962665
                                             abne_w01 |   -.297045   .0461889    -6.43   0.000    -.3875736   -.2065163
                                             tang_w01 |   -.838332   .0486385   -17.24   0.000    -.9336617   -.7430022
                                             prof_w01 |   .4818726   .0739659     6.51   0.000     .3369021    .6268431
                                           xrd_at_w01 |   .7971725   .2296823     3.47   0.001     .3470035    1.247341
                                              LEV_w01 |  -8.410532      .1946   -43.22   0.000    -8.791941   -8.029123
                                             g_gdpcap |  -.0231236   .0048162    -4.80   0.000    -.0325632   -.0136841
                                            Inflation |   .0001327   .0002965     0.45   0.654    -.0004484    .0007138
                                          lawandorder |  -.0613917   .0307742    -1.99   0.046     -.121708   -.0010754
                                           corruption |  -.0765255   .0219898    -3.48   0.001    -.1196248   -.0334262
                                             stmktcap |  -.0044963   .0006394    -7.03   0.000    -.0057495   -.0032432
                                               prbond |   .0034049   .0012427     2.74   0.006     .0009693    .0058405
                                               dbagdp |   .0001205   .0007238     0.17   0.868    -.0012981    .0015392
                                                      |
                               c.dbagdp#c.KS_oi_5_w01 |   .0000461   .0000219     2.11   0.035     3.22e-06     .000089
                                                      |
                                                Ind49 |
                                         Agriculture  |   .4941466   .2673099     1.85   0.065    -.0297711    1.018064
                                       Food Products  |   .5249754    .233292     2.25   0.024     .0677316    .9822193
                                      Candy and Soda  |   1.018373   .2931176     3.47   0.001     .4438727    1.592873
                                Alchoholic Beverages  |   .7657073    .265569     2.88   0.004     .2452015    1.286213
                                    Tobacco Products  |   .8149379   .5103465     1.60   0.110     -.185323    1.815199
                               Recreational Products  |   .6318073   .2544344     2.48   0.013     .1331251     1.13049
                                       Entertainment  |    .603786   .2402789     2.51   0.012     .1328481    1.074724
                             Printing and Publishing  |   .4176964   .2461339     1.70   0.090    -.0647172    .9001101
                                      Consumer Goods  |   .6839537    .231024     2.96   0.003      .231155    1.136752
                                             Apparel  |   .7099385   .2364263     3.00   0.003     .2465514    1.173326
                                          Healthcare  |  -.0163825   .2619527    -0.06   0.950    -.5298003    .4970352
                                   Medical Equipment  |   .3302004   .2339432     1.41   0.158    -.1283198    .7887207
                             Pharmaceutical Products  |   .2109182   .2254983     0.94   0.350    -.2310504    .6528868
                                           Chemicals  |   .4494764   .2273176     1.98   0.048     .0039421    .8950107
                         Rubber and Plastic Products  |   .1563614   .2474626     0.63   0.527    -.3286563    .6413791
                                            Textiles  |   .7984527   .2524835     3.16   0.002     .3035942    1.293311
                              Construction Materials  |   .5034542   .2311519     2.18   0.029     .0504048    .9565037
                                        Construction  |   .4336916   .2384028     1.82   0.069    -.0335693    .9009525
                                   Steel Works, Etc.  |   .7953972   .2342594     3.40   0.001     .3362572    1.254537
                                 Fabricated Products  |   .2460185   .2863962     0.86   0.390    -.3153077    .8073447
                                           Machinery  |   .1575207   .2263105     0.70   0.486    -.2860398    .6010812
                            Electrical Equipment One  |   .3201829   .2342249     1.37   0.172    -.1388895    .7792554
                              Automobiles and Trucks  |   .5433898   .2373046     2.29   0.022     .0782813    1.008498
                                            Aircraft  |   .1748933   .3257299     0.54   0.591    -.4635256    .8133122
                    Shipbuilding, Railroad Equipment  |   .4984448   .3711194     1.34   0.179    -.2289359    1.225826
                                             Defense  |   .9110807   .6432799     1.42   0.157    -.3497247    2.171886
                                     Precious Metals  |   .7551503   .2473642     3.05   0.002     .2703254    1.239975
            Non_Metallic and Industrial Metal Mining  |   .6052895   .2361843     2.56   0.010     .1423768    1.068202
                                                Coal  |  -.0746437   .2852365    -0.26   0.794     -.633697    .4844096
                           Petroleum and Natural Gas  |   .7276036   .2333674     3.12   0.002     .2702118    1.184995
                                   Personal Services  |   .3326592   .2804095     1.19   0.235    -.2169333    .8822517
                                   Business Services  |   .3680587    .226705     1.62   0.104    -.0762749    .8123923
                                           Computers  |   .7424846   .2352304     3.16   0.002     .2814416    1.203528
                                   Computer Software  |   .5784136   .2230003     2.59   0.009      .141341    1.015486
                            Electrical Equipment Two  |   .5789206   .2246373     2.58   0.010     .1386396    1.019202
                         Measuring and Lab Equipment  |   .4451445   .2433709     1.83   0.067    -.0318536    .9221426
                                   Business Supplies  |   .3664276    .247165     1.48   0.138    -.1180069    .8508622
                                 Shipping Containers  |   .3193641   .3588074     0.89   0.373    -.3838855    1.022614
                                           Wholesale  |   .7041549   .2267843     3.10   0.002     .2596657    1.148644
                                              Retail  |   .7566017   .2275703     3.32   0.001      .310572    1.202631
                         Restaurants, Hotels, Motels  |   .2948672   .2458327     1.20   0.230     -.186956    .7766905
                                       Miscellaneous  |   .4948622   .3111194     1.59   0.112    -.1149206    1.104645
                                                      |
                                                fyear |
                                                1991  |   .0478538   .0553452     0.86   0.387    -.0606209    .1563284
                                                1992  |   .2314154   .0645841     3.58   0.000     .1048329    .3579979
                                                1993  |   .2884336   .0684913     4.21   0.000     .1541931     .422674
                                                1994  |   .2485886   .0736259     3.38   0.001     .1042845    .3928927
                                                1995  |   .2402825   .0767248     3.13   0.002     .0899046    .3906604
                                                1996  |    .389684   .0808584     4.82   0.000     .2312044    .5481636
                                                1997  |   .4868546   .0882609     5.52   0.000     .3138664    .6598428
                                                1998  |   .6492823   .0937267     6.93   0.000     .4655814    .8329832
                                                1999  |   .8178225   .0985749     8.30   0.000     .6246191    1.011026
                                                2000  |   .9246871   .0994937     9.29   0.000     .7296831    1.119691
                                                2001  |    .679545   .0926606     7.33   0.000     .4979336    .8611565
                                                2002  |   .7378798   .0897632     8.22   0.000     .5619472    .9138123
                                                2003  |   .8286484   .0906864     9.14   0.000     .6509062    1.006391
                                                2004  |   .9388822   .0931766    10.08   0.000     .7562593    1.121505
                                                2005  |   .9550393   .0946732    10.09   0.000     .7694833    1.140595
                                                2006  |   .8926401   .1006127     8.87   0.000     .6954428    1.089837
                                                2007  |   .9118378   .1076076     8.47   0.000     .7009307    1.122745
                                                2008  |   1.053451   .1012435    10.41   0.000     .8550172    1.251885
                                                2009  |   .8199462   .0985915     8.32   0.000     .6267105    1.013182
                                                2010  |   1.037379   .1029246    10.08   0.000     .8356502    1.239107
                                                2011  |   1.111155   .0982362    11.31   0.000     .9186153    1.303694
                                                2012  |   .9618468   .1005202     9.57   0.000     .7648308    1.158863
                                                2013  |   .9214399   .1016192     9.07   0.000       .72227     1.12061
                                                2014  |   .7480806   .1041488     7.18   0.000     .5439526    .9522086
                                                2015  |   .7575959    .109936     6.89   0.000     .5421253    .9730666
                                                      |
                                                fic_n |
                                                 AUT  |  -.6126646   .2900246    -2.11   0.035    -1.181102   -.0442268
                                                 BEL  |  -1.685696   .4077713    -4.13   0.000    -2.484913   -.8864793
                                                 BRA  |  -.9469862   .2560525    -3.70   0.000     -1.44884   -.4451325
                                                 CAN  |   .2812779   .1605531     1.75   0.080    -.0334003    .5959561
                                                 CHE  |   .1463367   .1948234     0.75   0.453    -.2355101    .5281835
                                                 CHL  |  -1.409904   .3141855    -4.49   0.000    -2.025696   -.7941114
                                                 CHN  |   .6308343   .1248283     5.05   0.000     .3861752    .8754933
                                                 COL  |  -.8460806   .5064874    -1.67   0.095    -1.838778    .1466166
                                                 CYP  |  -1.017508   .6213726    -1.64   0.102    -2.235376    .2003598
                                                 DEU  |  -.5578331   .1239633    -4.50   0.000    -.8007968   -.3148695
                                                 DNK  |  -1.218518   .2635688    -4.62   0.000    -1.735103   -.7019322
                                                 ESP  |  -2.435722   .4800787    -5.07   0.000    -3.376659   -1.494785
                                                 FIN  |  -1.238112   .3629535    -3.41   0.001    -1.949488   -.5267367
                                                 FRA  |  -1.835735   .1415487   -12.97   0.000    -2.113165   -1.558305
                                                 GBR  |   .0204194   .0948368     0.22   0.830    -.1654573    .2062961
                                                 GRC  |    .242073   .1862281     1.30   0.194    -.1229274    .6070733
                                                 HKG  |    1.26579   .3591318     3.52   0.000     .5619041    1.969675
                                                 HRV  |  -.5900594   .4385059    -1.35   0.178    -1.449515    .2693963
                                                 HUN  |  -.6667466   .4967467    -1.34   0.180    -1.640352     .306859
                                                 IDN  |   -.198277   .2094094    -0.95   0.344     -.608712    .2121579
                                                 IND  |  -.4956916    .153169    -3.24   0.001    -.7958973   -.1954858
                                                 IRL  |  -.4325902   .3991141    -1.08   0.278    -1.214839     .349659
                                                 ISR  |  -.1340825   .1638583    -0.82   0.413    -.4552388    .1870739
                                                 ITA  |  -1.652573   .3132525    -5.28   0.000    -2.266537    -1.03861
                                                 JPN  |  -.0062688   .0881769    -0.07   0.943    -.1790923    .1665548
                                                 KOR  |   .3059268   .1038743     2.95   0.003     .1023369    .5095166
                                                 MEX  |   .1573826   .2688252     0.59   0.558    -.3695052    .6842704
                                                 MYS  |  -.3004064   .1277227    -2.35   0.019    -.5507382   -.0500746
                                                 NLD  |  -.2326297   .2123913    -1.10   0.273    -.6489091    .1836496
                                                 NOR  |  -.3996846   .2046473    -1.95   0.051    -.8007859    .0014167
                                                 PER  |  -.1124155   .2952695    -0.38   0.703     -.691133     .466302
                                                 PHL  |   .1863668   .2326802     0.80   0.423     -.269678    .6424116
                                                 POL  |  -1.549461   .1876713    -8.26   0.000     -1.91729   -1.181632
                                                 PRT  |     1.0819   .7159941     1.51   0.131    -.3214222    2.485223
                                                 RUS  |  -.2955311   .2965418    -1.00   0.319    -.8767422    .2856801
                                                 SGP  |   .2875965   .1380747     2.08   0.037     .0169751    .5582179
                                                 SWE  |  -.1906895    .125562    -1.52   0.129    -.4367865    .0554075
                                                 THA  |   .0479262   .1623427     0.30   0.768    -.2702597    .3661121
                                                 TUR  |   .1805885   .1815414     0.99   0.320    -.1752261    .5364031
                                                 USA  |   -.032005   .0971921    -0.33   0.742    -.2224979     .158488
                                                 ZAF  |  -.4356978   .2107157    -2.07   0.039     -.848693   -.0227026
            ------------------------------------------+----------------------------------------------------------------
                                                /cut1 |  -1.445463   .3438674                     -2.119431   -.7714953
                                                /cut2 |  -.3622056   .3442741                     -1.036971    .3125593
            -----------------------------------------------------------------------------------------------------------
            then I run the margins command for cash flow volatility
            Code:
            margins,dydx(KS_oi_5_w01)
            
            Average marginal effects                        Number of obs     =    206,445
            Model VCE    : Robust
            
            dy/dx w.r.t. : KS_oi_5_w01
            1._predict   : Pr(DebtMat_D==1), predict(pr outcome(1))
            2._predict   : Pr(DebtMat_D==2), predict(pr outcome(2))
            3._predict   : Pr(DebtMat_D==3), predict(pr outcome(3))
            
            ------------------------------------------------------------------------------
                         |            Delta-method
                         |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
            -------------+----------------------------------------------------------------
            KS_oi_5_w01  |
                _predict |
                      1  |  -.0017086   .0001191   -14.35   0.000     -.001942   -.0014752
                      2  |   .0005176   .0000382    13.54   0.000     .0004426    .0005925
                      3  |    .001191   .0000825    14.44   0.000     .0010293    .0013527
            ------------------------------------------------------------------------------
            but when I run the margin command for interaction term
            Code:
             margins,dydx(c.dbagdp#c.KS_oi_5_w01)
            invalid dydx() option;
            levels of interactions not allowed
            Could you please recommend how to figure out the marginal effects for the interaction terms first before interpreting?

            Thanks
            Huyen
            Last edited by Huyen Nguyen VUW; 24 Jan 2020, 18:52.

            Comment


            • #7
              Could you please recommend how to figure out the marginal effects for the interaction terms first before interpreting?
              There is no such thing as the marginal effect of an interaction term. That's why Stata refuses to calculate it for you.

              What exactly is it you want to calculate--describe it carefully and in detail. Whatever it is, it isn't a marginal effect of an interaction term.

              The usual things one calculates from models like this are marginal effects of either of the interacted variables at selected values of the other. And often the best way to understand a model like this is to graph those results, which is easily done with -marginsplot-.

              Comment


              • #8
                Hi Clyde,

                From the regression in the reply #6, the coefficients of cash flow volatility (KS_oi_5_w01) is positive. So can I say the probability of firms using shorter(longer) maturity of debt increases (decreases) with cash flow volatility?
                Given the coefficient of the interaction term ( c.dbagdp#c.KS_oi_5_w01) is positive, how can I interpret this sign because both of them are continuous variables?

                Also, after getting the marginal effects of KS_oi_5_w01 on, let's say category 1 of debt maturity, which is -.0017086 and the standard deviation of cash flow volatility in my sample is 12.20564, I could say: a one standard deviation increase in cash flow volatility implies a 2.08% (=0.0017086*12.20564) decrease in the probability of a firm using long-term debt.

                So I would like to have something similar by calculating the marginal effects of the interaction term. However, it is impossible now.

                Back to my question, how can I interpret the sign of the interaction term in the regression in reply #6?

                Regards.
                Huyen

                Comment


                • #9
                  For the moment, let's put aside the complications introduced by the ordinal logistic regression, and just imagine that there were a single outcome variable with a linear regression.

                  The coefficient of KS_oi_5_w01 is 0.010 (I'm going to round everything to 3 decimal places here) and that would mean that the rate of increase of the outcome per unit increase in KS_oi_5_w01 when dbaggdp = 0 is 0.010. Similarly, the rate of increase of the outcome per unit increase of dbaggdp when KS_oi_5_w01 = 0 is equal to the coefficient of dbagdp, namely 0.001. Now these marginal effects that are conditional on the other variable being zero may or may not be of interest, depending on whether KS_oi_5_w01 = 0 and dbaggdp = 0 are interesting situations in the real world (or even possible at all--I have no idea what these variables mean. In general we would be more interested in the effects of these variables on the outcome at ranges of values of each other. So, for example, assuming that dbaggdp = 500 is a realistic and interesting possibility in the real world, we might want to know what the marginal effect of KS_oi_5_w01 is when dbaggdp = 500. This is where the interaction coefficient comes in. The rate of increase of the outcome per unit increase in KS_oi_5_w01 when dbaggdp = 5 is 0.010 + 500* 0.0000461 = 0.033. You can do analogous calculations for any chosen values of dbagdp, and you can do something similar for marginal effects of dbagdp when KS_oi_5_w01 takes on different values.

                  Now, the situation is complicated by the ordinal logistic outcome with three categories. The coefficient is no longer a marginal effect. Moreover, if the probability of one of the outcomes increases as some predictor increases, then the probability of some other outcome must necessarily decrease since the total of all the outcome probabilities must be 1.0. The actual calculations of the marginal effects on each of the outcome probabilities is, therefore, somewhat complicated. Fortunately, -margins- does the work for you.

                  Now the -margins- output you show in #6 is the average marginal effect of KS_oi_5_w01, the average being taken over all values of dbaggdp in your estimation sample. That may or may not be useful or interesting. I think that the best way to gain an understanding of this kind of model is graphically. I recommend you do the following. First pick an interesting range of values of KS_oi_5_w01 and dbaggdp. For the purposes of illustration I'm going to assume these ranges of values are (10 20 30 40 50) and (200 400 600 800), respectively. Then run these commands:

                  Code:
                  margins, at(KS_oi_5_w01 = (10(10)50) dbaggdp = (200(200)800))
                  marginsplot, name(expected_probabilities, replace)
                  
                  margins, dydx(KS_oi_5_w01) at(dbaggdp = (200(200)800))
                  marginsplot, name(marginal_effects_KS_oi_5_w01, replace)
                  and study the graphs. You might also want to run
                  Code:
                  margins, dydx(dbaggdp) at(KS_oi_5_w01 = (200(200)800))
                  marginsplot, name(marginal_effects_dbaggdp, replace)
                  You will learn more from spending 5 minutes with those graphs than you will get studying the regression output for 5 days.

                  By the way, let's review why there is no such thing as the marginal effect of an interaction term. At the most superficial level, a marginal effect means the rate of change in the outcome per unit change in the predictor, everything else held constant. Well, by the very nature of an interaction term, it is impossible for the interaction term to change when its constituents are held constant. Taking it a step farther, realize that a unit change in the interaction term could be the result of infinitely many different combinations of changes in KS_oi_5_w01 and changes in dbaggdp. But each of those combinations would produce a different change in the outcome--so there is no way to select which of those infinitely many outcome changes would represent the marginal effect. That is why there is no such thing as the marginal effect of an interaction term in any interaction model.

                  Comment


                  • #10
                    Thank you for your suggestions, Clyde. I will play around with the graphs and get back to you if need help. Thank you so much.

                    Huyen

                    Comment


                    • #11
                      Hi Clyde,

                      If I put aside the magnitude of the coefficients of the interaction term, what could we say about its sign (positive)?

                      Thanks
                      Huyen

                      Comment


                      • #12
                        Not very much. You can't say very much about the sign of a non-interaction variable in an ordered logistic regression either. The complication arises because the sum of the predicted probabilities for the three outcomes must sum to 1, so they cannot all go in the same direction. So some of them will go the same way as the sign of the coefficient, and some will go the opposite way. And which is which really depends on the values of the cutpoint estimates. This kind of interpretation, which is so simple in linear regression, is really just not feasible for ordered logistic (nor for multinomial logistic) analysis.

                        Comment

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