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  • Matching of Cases to reduce sample size of logit regression

    Hi everyone,

    I'm working on a study to investigate the impact of firm performance on probability of takeover. I will be using a logit model, with target = 1 or 0 as the dependent variable, and other firm characteristics to obtain results. However, currently my ratio of targets to non-targets is 96 : 1315, which is quite skewed.

    Hence, I'm looking to reduce my non-targets sample to a smaller number before running the regression, probably by matching 1-2 non-targets to every target. I plan to match the targets based on the year and reit_id but i'm not quite sure how to do this. Below is my code for a small portion of my data. The column target is the dependent variable, where i hope to reduce the number target = 0.

    Thanks for your help in advance.


    Code:
    entityname    entityid    target    year    reit_id    roa    spalpha    ebitdamargin    market_ta
    Campus Crest Communities, Inc.    4258761    1    2014    Specialty    .579    -0.51    37.455    40.21625
    Monogram Residential Trust, Inc.    4190766    1    2016    Multifamily    .179    0.07    47.322    56.40852
    Rayonier Inc.    4062541    0    2014    Specialty    1.811    -0.72    34.616    144.3895
    CyrusOne Inc.    4332673    0    2014    Specialty    1.657    0.29    46.479    67.78162
    American Residential Properties, Inc.    4383076    1    2014    Specialty    -.778    0.07    32.278    41.56983
    Quality Care Properties, Inc.    4745972    1    2017    Health Care    2.141    -0.81    90.71    29.4966
    New Senior Investment Group Inc.    4544851    0    2016    Health Care    .208    -0.09    41.152    28.49409
    Gladstone Land Corporation    4264067    0    2014    Specialty    1.08    -0.92    50.964    54.68895
    Independence Realty Trust, Inc.    4235858    0    2016    Multifamily    -.246    0.24    19.267    47.55272
    Front Yard Residential Corporation    4345051    0    2015    Specialty    .982    -0.51    19.431    28.1446
    Bluerock Residential Growth REIT, Inc.    4214866    0    2017    Multifamily    -1.42    -0.72    13.368    14.52915
    New Senior Investment Group Inc.    4544851    0    2017    Health Care    1.07    -0.74    41.344    24.76231
    Gladstone Land Corporation    4264067    0    2015    Specialty    1.552    -0.40    64.09    37.79842
    Silver Bay Realty Trust Corp.    4335231    1    2016    Specialty    .954    0.07    44.124    49.76474
    CatchMark Timber Trust, Inc.    4108902    0    2015    Specialty    -.518    -0.04    32.389    73.57886
    Gladstone Commercial Corporation    4088076    0    2014    Diversified    2.586    -0.15    80.214    44.81316
    Trade Street Residential, Inc.    4094472    1    2014    Multifamily    .444    0.46    40.342    49.62671
    Gladstone Land Corporation    4264067    0    2016    Specialty    1.624    0.46    71.098    33.73792
    Associated Estates Realty Corporation    103102    1    2014    Multifamily    1.62    0.61    51.628    91.29086
    NexPoint Residential Trust, Inc.    4561930    0    2016    Multifamily    1.362    0.97    43.274    45.40438
    NexPoint Residential Trust, Inc.    4561930    0    2017    Multifamily    .795    0.45    43.014    55.72662
    UDR, Inc.    103025    0    2014    Multifamily    1.101    0.50    59.705    115.1405
    CatchMark Timber Trust, Inc.    4108902    0    2016    Specialty    -.383    -0.09    30.576    61.54402
    Gladstone Commercial Corporation    4088076    0    2015    Diversified    2.622    -0.29    82.294    41.37527
    American Campus Communities, Inc.    4092925    0    2014    Specialty    1.721    0.41    48.367    76.2162
    Mid-America Apartment Communities, Inc.    103123    0    2014    Multifamily    2.192    0.31    54.732    82.39773
    Lexington Realty Trust    103128    0    2014    Diversified    2.94    0.06    81.272    68.14964
    NorthStar Realty Europe Corp.    4608576    0    2016    Office    -.167    0.00    41.071    37.73274
    Camden Property Trust    103094    0    2014    Multifamily    2.653    0.42    56.397    105.8357
    Apartment Investment and Management Company    103180    0    2014    Multifamily    2.712    0.60    56.818    89.20546
    Gladstone Land Corporation    4264067    0    2017    Specialty    1.822    0.48    73.489    40.06698
    Global Net Lease, Inc.    4307540    0    2016    Diversified    1.613    -0.15    76.801    53.82782
    Global Net Lease, Inc.    4307540    0    2017    Diversified    1.844    -0.53    78.085    45.57275
    American Homes 4 Rent    4392539    0    2015    Specialty    .424    -0.11    43.443    51.29628
    Pennsylvania Real Estate Investment Trust    102991    0    2014    Regional Mall    1.859    0.21    50.725    63.55355
    One Liberty Properties, Inc.    102988    0    2014    Diversified    3.427    0.21    73.748    63.40358
    Home Properties, Inc.    103183    1    2014    Multifamily    2.995    0.31    59.654    84.33441
    Apartment Investment and Management Company    103180    0    2012    Multifamily    1.922    0.23    55.875    61.53297
    New Senior Investment Group Inc.    4544851    0    2015    Health Care    -.109    -0.92    40.188    27.92127
    MGM Growth Properties LLC    4674180    0    2017    Specialty    2.33    0.31    82.439    19.96539
    Preferred Apartment Communities, Inc.    4263486    0    2012    Multifamily    1.318    0.52    46.964    33.54093
    CatchMark Timber Trust, Inc.    4108902    0    2017    Specialty    -.21    0.18    29.093    77.03358
    Rayonier Inc.    4062541    0    2015    Specialty    2.179    -0.38    36.139    117.6844
    UDR, Inc.    103025    0    2012    Multifamily    .682    -0.20    59.412    86.96828
    Wheeler Real Estate Investment Trust, Inc.    4305469    0    2014    Shopping Center    -1.892    -0.11    24.25    14.47827
    Apartment Investment and Management Company    103180    0    2010    Multifamily    .972    1.07    48.615    41.19895
    Preferred Apartment Communities, Inc.    4263486    0    2017    Multifamily    1.309    0.44    58.694    24.01128
    Lexington Realty Trust    103128    0    2015    Diversified    2.936    -0.55    80.284    49.2753
    Rouse Properties, Inc.    4298147    1    2015    Regional Mall    1.486    -0.33    56.213    33.42612
    UDR, Inc.    103025    0    2013    Multifamily    .954    -0.47    59.396    86.26359
    Colonial Properties Trust    103076    1    2012    Multifamily    1.977    -0.03    55.763    57.36412
    QTS Realty Trust, Inc.    4405219    0    2014    Specialty    2.425    0.56    39.725    89.93388
    Apartment Investment and Management Company    103180    0    2013    Multifamily    2.503    -0.52    56.902    62.18889
    Washington Real Estate Investment Trust    103036    0    2014    Diversified    1.94    0.19    55.25    88.9749
    AvalonBay Communities, Inc.    103145    0    2014    Multifamily    2.958    0.58    65.601    133.6737
    Healthcare Realty Trust Incorporated    103057    0    2014    Health Care    2.364    0.45    59.304    97.91383
    Gladstone Commercial Corporation    4088076    0    2012    Diversified    3.239    -0.06    83.093    35.79676
    CoreSite Realty Corporation    4258680    0    2014    Specialty    2.757    0.28    46.367    79.06402
    American Campus Communities, Inc.    4092925    0    2015    Specialty    1.654    -0.01    48.54    77.32224
    Gladstone Commercial Corporation    4088076    0    2016    Diversified    2.455    0.50    81.015    60.98448
    Digital Realty Trust, Inc.    4094311    0    2014    Specialty    2.63    0.52    55.927    94.38674
    NorthStar Realty Finance Corp.    4092549    1    2015    Diversified    2.471    -0.93    47.505    20.25767
    Apartment Investment and Management Company    103180    0    2015    Multifamily    2.616    0.13    57.883    102.2728
    InfraREIT, Inc. (REIT)    4573482    0    2016    Specialty    3.656    -0.05    87.303    41.77341
    Cogdell Spencer Inc.    4104525    1    2010    Health Care    1.354    0.08    25.996    46.61516
    Camden Property Trust    103094    0    2016    Multifamily    2.639    0.11    56.562    122.0128
    American Homes 4 Rent    4392539    0    2014    Specialty    -.017    -0.01    37.351    58.19209
    Wheeler Real Estate Investment Trust, Inc.    4305469    0    2015    Shopping Center    -1.149    -1.50    45.911    41.35297
    Pennsylvania Real Estate Investment Trust    102991    0    2016    Regional Mall    2.274    -0.41    55.312    50.39394
    CIM Commercial Trust Corporation    4543503    0    2017    Office    1.073    0.63    36.596    62.57856
    Equity Residential    103054    0    2014    Multifamily    2.515    0.59    64.383    113.581
    Investors Real Estate Trust    107231    0    2013    Multifamily    2.9    -0.50    58.091    52.25985
    Washington Real Estate Investment Trust    103036    0    2013    Diversified    1.988    -0.80    57.383    78.9179
    PS Business Parks, Inc.    102999    0    2014    Diversified    3.514    -0.03    62.349    96.14012
    Medical Properties Trust, Inc.    4095909    0    2014    Health Care    2.814    0.17    64.68    63.9744
    UDR, Inc.    103025    0    2016    Multifamily    1.466    -0.13    62.788    126.9551
    UDR, Inc.    103025    0    2010    Multifamily    .374    0.70    55.599    77.62515
    American Assets Trust, Inc.    4270741    0    2014    Diversified    2.771    0.35    57.604    89.59715
    Healthcare Trust of America, Inc.    4132396    0    2014    Health Care    1.928    0.53    61.652    111.1654
    Wheeler Real Estate Investment Trust, Inc.    4305469    0    2017    Shopping Center    1.265    -0.77    58.985    19.0675
    Pennsylvania Real Estate Investment Trust    102991    0    2017    Regional Mall    1.8    -0.98    54.761    32.14258
    One Liberty Properties, Inc.    102988    0    2015    Diversified    3.369    -0.15    72.37    54.07995
    Farmland Partners Inc.    4426904    0    2015    Specialty    1.424    0.03    50.33    38.09379
    Washington Real Estate Investment Trust    103036    0    2015    Diversified    1.83    -0.01    56.267    84.21301
    One Liberty Properties, Inc.    102988    0    2012    Diversified    3.33    0.36    75.484    61.89199
    CBL & Associates Properties, Inc.    103092    0    2014    Regional Mall    3.824    0.02    65.297    50.10408

  • #2
    1) Matching might or might not be a good idea, but I can't think of any reason why reducing your sample size, that is, *discarding information,* would be desirable. There are some issues with bias in logit estimation with rare events, but the issue is *number* of events, not proportion of events. See https://statisticalhorizons.com/logi...or-rare-events
    See also -firthlogit- at SSC, which would be fine to use, but would likely not make a difference with 96 events.

    2) Please look at how your data example looks online, and you'll see that it would be very hard for anyone to use. The StataList FAQ recommend using -dataex- to show example data. You'll want to use that if you post data again.

    3) Your description references "takeovers" and "targets," which is a big confusing. A "target," at least in ordinary usage of the word, might or might not become a "takeover," as the attempt to take over a firm might or might not succeed. It probably doesn't matter for your current question, but I can imagine other contexts in which the distinction of a target firm vs. an actual takeover might matter

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