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  • Calculate odds ratio from linear regression coefficient with binary dependt variable?

    Hello everyone!

    I have a multiple linear regression model with, among others, a categorical variable for gender (male / female) which I use to predict the probability of the respondent having submitted an idea (yes/no).
    Female is used as the baseline category. Is there a way to use the coeffienct from men to calculate the odds ration between men and women?

    I assume that it should be possible since the DV is dichotomous and hence the coefficient is in effect a measure of probability? If so, how would the procedure to calculate this be?

    The coefficient for men are: .2485926

    Thanks for all the fantastic help provided in this forum!

  • #2
    Is there a reason for not using logistic regression? Like:
    Code:
    logistic IDEA i.MALE X2 X3 X4
    would provide the odds ratio directly in the output.

    Comment


    • #3
      I suppose that there's a reason for your fitting a linear probability model, but I agree with Ken that if you're interested in odds ratios, then -logit- seems the more straightforward approach.

      Anyway, you could consider something like the following.

      .ÿ
      .ÿversionÿ17.0

      .ÿ
      .ÿclearÿ*

      .ÿ
      .ÿsetÿseedÿ`=strreverse("1606170")'

      .ÿ
      .ÿquietlyÿsetÿobsÿ250

      .ÿ
      .ÿgenerateÿbyteÿoutÿ=ÿruniform()ÿ<ÿ0.5

      .ÿgenerateÿbyteÿsexÿ=ÿmod(_n,ÿ2)

      .ÿgenerateÿdoubleÿpreÿ=ÿruniform(-0.5,ÿ0.5)

      .ÿ
      .ÿ*
      .ÿ*ÿBeginÿhere
      .ÿ*
      .ÿregressÿoutÿi.sexÿc.preÿ//ÿ,ÿvce(robust)

      ÿÿÿÿÿÿSourceÿ|ÿÿÿÿÿÿÿSSÿÿÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿMSÿÿÿÿÿÿNumberÿofÿobsÿÿÿ=ÿÿÿÿÿÿÿ250
      -------------+----------------------------------ÿÿÿF(2,ÿ247)ÿÿÿÿÿÿÿ=ÿÿÿÿÿÿ0.48
      ÿÿÿÿÿÿÿModelÿ|ÿÿÿ.24304012ÿÿÿÿÿÿÿÿÿ2ÿÿÿ.12152006ÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿ=ÿÿÿÿ0.6168
      ÿÿÿÿResidualÿ|ÿÿ62.0009599ÿÿÿÿÿÿÿ247ÿÿ.251016032ÿÿÿR-squaredÿÿÿÿÿÿÿ=ÿÿÿÿ0.0039
      -------------+----------------------------------ÿÿÿAdjÿR-squaredÿÿÿ=ÿÿÿ-0.0042
      ÿÿÿÿÿÿÿTotalÿ|ÿÿÿÿÿÿ62.244ÿÿÿÿÿÿÿ249ÿÿ.249975904ÿÿÿRootÿMSEÿÿÿÿÿÿÿÿ=ÿÿÿÿ.50102

      ------------------------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
      -------------+----------------------------------------------------------------
      ÿÿÿÿÿÿÿ1.sexÿ|ÿÿ-.0572617ÿÿÿ.0634409ÿÿÿÿ-0.90ÿÿÿ0.368ÿÿÿÿ-.1822159ÿÿÿÿ.0676925
      ÿÿÿÿÿÿÿÿÿpreÿ|ÿÿÿ-.049069ÿÿÿ.1133506ÿÿÿÿ-0.43ÿÿÿ0.665ÿÿÿÿÿ-.272326ÿÿÿÿÿ.174188
      ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ.5609682ÿÿÿ.0448679ÿÿÿÿ12.50ÿÿÿ0.000ÿÿÿÿÿ.4725956ÿÿÿÿ.6493407
      ------------------------------------------------------------------------------

      .ÿmarginsÿsex,ÿpost

      PredictiveÿmarginsÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ250
      ModelÿVCE:ÿOLS

      Expression:ÿLinearÿprediction,ÿpredict()

      ------------------------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿDelta-method
      ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿMarginÿÿÿstd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
      -------------+----------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿsexÿ|
      ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.5606309ÿÿÿ.0448358ÿÿÿÿ12.50ÿÿÿ0.000ÿÿÿÿÿ.4723215ÿÿÿÿ.6489402
      ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.5033691ÿÿÿ.0448358ÿÿÿÿ11.23ÿÿÿ0.000ÿÿÿÿÿ.4150598ÿÿÿÿ.5916785
      ------------------------------------------------------------------------------

      .ÿnlcomÿOR:ÿexp(logit(_b[1.sex])ÿ-ÿlogit(_b[0.sex]))

      ÿÿÿÿÿÿÿÿÿÿOR:ÿexp(logit(_b[1.sex])ÿ-ÿlogit(_b[0.sex]))

      ------------------------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
      -------------+----------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿÿORÿ|ÿÿÿ.7943382ÿÿÿ.2030884ÿÿÿÿÿ3.91ÿÿÿ0.000ÿÿÿÿÿ.3962921ÿÿÿÿ1.192384
      ------------------------------------------------------------------------------

      .ÿ//ÿor
      .ÿnlcomÿOR:ÿ(ÿ_b[1.sex]ÿ/ÿ(1ÿ-ÿ_b[1.sex])ÿ)ÿ/ÿ(ÿ_b[0.sex]ÿ/ÿ(1ÿ-ÿ_b[0.sex])ÿ)

      ÿÿÿÿÿÿÿÿÿÿOR:ÿ(ÿ_b[1.sex]ÿ/ÿ(1ÿ-ÿ_b[1.sex])ÿ)ÿ/ÿ(ÿ_b[0.sex]ÿ/ÿ(1ÿ-ÿ_b[0.sex])ÿ)

      ------------------------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
      -------------+----------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿÿORÿ|ÿÿÿ.7943382ÿÿÿ.2030884ÿÿÿÿÿ3.91ÿÿÿ0.000ÿÿÿÿÿ.3962921ÿÿÿÿ1.192384
      ------------------------------------------------------------------------------

      .ÿ
      .ÿlogitÿoutÿi.sexÿc.pre,ÿorÿnolog

      LogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿÿÿÿ250
      ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿLRÿchi2(2)ÿÿÿÿ=ÿÿÿ0.98
      ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿ=ÿ0.6134
      Logÿlikelihoodÿ=ÿ-172.28576ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿPseudoÿR2ÿÿÿÿÿ=ÿ0.0028

      ------------------------------------------------------------------------------
      ÿÿÿÿÿÿÿÿÿoutÿ|ÿOddsÿratioÿÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
      -------------+----------------------------------------------------------------
      ÿÿÿÿÿÿÿ1.sexÿ|ÿÿÿ.7941829ÿÿÿ.2019731ÿÿÿÿ-0.91ÿÿÿ0.365ÿÿÿÿÿ.4824437ÿÿÿÿ1.307358
      ÿÿÿÿÿÿÿÿÿpreÿ|ÿÿÿ.8203934ÿÿÿ.3730382ÿÿÿÿ-0.44ÿÿÿ0.663ÿÿÿÿÿ.3364924ÿÿÿÿÿ2.00018
      ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ1.277965ÿÿÿ.2307145ÿÿÿÿÿ1.36ÿÿÿ0.174ÿÿÿÿÿ.8971177ÿÿÿÿ1.820492
      ------------------------------------------------------------------------------
      Note:ÿ_consÿestimatesÿbaselineÿodds.

      .ÿ
      .ÿexit

      endÿofÿdo-file


      .


      I trust that your predictions aren't beyond the pale.

      Comment

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