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  • Interpretation of moderation effects in inverted U-shaped relationship

    Dear Statalist,

    I have the following issue:

    I want to investigate the moderation effect of absorptive capacity in form of research and development expenses on the relationship between innovativeness(number_patents) and CVC actvities(cvc1). To test an inverted U-shape, I also integrated the squared value cvc2.

    The results are the following:

    Code:
     xtreg number_patents c.cvc1##c.cvc1##c.ResearchandDevelopmentExpense rdi CurrentAssetsTotal log_industry_dynam
    > ism StandardIndustryClassification q_tobin i.fyear, re cluster(gvkey)
    
    Random-effects GLS regression                   Number of obs     =        475
    Group variable: gvkey                           Number of groups  =         84
    
    R-squared:                                      Obs per group:
         Within  = 0.2712                                         min =          1
         Between = 0.0562                                         avg =        5.7
         Overall = 0.1817                                         max =         14
    
                                                    Wald chi2(23)     =     181.65
    corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000
    
                                                                      (Std. err. adjusted for 84 clusters in gvkey)
    ---------------------------------------------------------------------------------------------------------------
                                                  |               Robust
                                   number_patents | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
    ----------------------------------------------+----------------------------------------------------------------
                                             cvc1 |   292.5542    106.482     2.75   0.006     83.85337    501.2551
                                                  |
                                    c.cvc1#c.cvc1 |  -21.40677   7.323167    -2.92   0.003    -35.75992   -7.053631
                                                  |
                    ResearchandDevelopmentExpense |   .0530701   .0231165     2.30   0.022     .0077626    .0983776
                                                  |
           c.cvc1#c.ResearchandDevelopmentExpense |  -.0260776   .0102224    -2.55   0.011     -.046113   -.0060421
                                                  |
    c.cvc1#c.cvc1#c.ResearchandDevelopmentExpense |   .0018291   .0009255     1.98   0.048     .0000152     .003643
                                                  |
                                              rdi |  -153.8569   299.8545    -0.51   0.608     -741.561    433.8471
                               CurrentAssetsTotal |  -.0025668    .005117    -0.50   0.616    -.0125959    .0074624
                            log_industry_dynamism |  -25.63305   14.76077    -1.74   0.082    -54.56362    3.297527
                   StandardIndustryClassification |   .0711053   .0726104     0.98   0.327    -.0712085    .2134191
                                          q_tobin |   27.10256   28.97523     0.94   0.350    -29.68784    83.89297
                                                  |
                                            fyear |
                                            2007  |  -21.67683   21.65702    -1.00   0.317     -64.1238    20.77015
                                            2008  |   29.23846   114.2926     0.26   0.798     -194.771    253.2479
                                            2009  |  -62.42921   52.84687    -1.18   0.237    -166.0072    41.14876
                                            2010  |   -35.8264   52.52186    -0.68   0.495    -138.7674    67.11455
                                            2011  |   61.59043   46.75624     1.32   0.188    -30.05012     153.231
                                            2012  |   121.7003   83.94128     1.45   0.147    -42.82156    286.2222
                                            2013  |   130.6375    87.6358     1.49   0.136    -41.12555    302.4005
                                            2014  |   11.53912   68.65388     0.17   0.867      -123.02    146.0983
                                            2015  |   47.76205   79.24387     0.60   0.547    -107.5531    203.0772
                                            2016  |  -57.21649   79.45166    -0.72   0.471    -212.9389    98.50591
                                            2017  |  -324.9182   85.68877    -3.79   0.000    -492.8651   -156.9713
                                            2018  |  -675.2418   197.5365    -3.42   0.001    -1062.406   -288.0773
                                            2019  |  -1053.773   234.9042    -4.49   0.000    -1514.177   -593.3691
                                                  |
                                            _cons |   66.27524   319.9227     0.21   0.836    -560.7618    693.3123
    ----------------------------------------------+----------------------------------------------------------------
                                          sigma_u |  574.47281
                                          sigma_e |  403.78588
                                              rho |  .66932552   (fraction of variance due to u_i)
    ---------------------------------------------------------------------------------------------------------------
    How can I interpret the interaction terms? Which value indicates if it is a positive or negative moderation effect? Until now, I used the squared interaction term (c.cvc1#c.cvc1#c.ResearchandDevelopmentExpense) as an indicator. As the regression coefficient is positive, I assumed a positive moderation. Is that the right approach?

    Thanks in advance!

    Kind regards,
    Henrik

  • #2
    http://www.maartenbuis.nl/wp/inter_q...ter_quadr.html
    ---------------------------------
    Maarten L. Buis
    University of Konstanz
    Department of history and sociology
    box 40
    78457 Konstanz
    Germany
    http://www.maartenbuis.nl
    ---------------------------------

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