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  • Zero Betas in HLM growth modeling

    How are significant betas very close to zero interpreted in HLM growth modeling? We have some significant near-zero betas in a 3-level (quadratic) model, significant for instantaneous rate of change and for acceleration/deceleration (e.g., one is 6.031e-3). There are no error message in the Stata output.

  • #2
    this sounds as though it might be an issue of the scaling of your time variable - maybe it is now in days but should be something larger (months? years?); if in days and you want weeks, then divide the days variable by 7 (etc.), save as a new variable and re-estimate

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    • #3
      Thank you!! We do already have the time variable in months (moving from spring of first grade to spring of eighth grade). I think I understand the gist of the impact of the scaling for the time variable, but I'm not seeing how the near-zero beta could be significant? Do you have any thoughts about that? THANK you again!

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      • #4
        I'm not seeing how the near-zero beta could be significant
        Why not? Statistical significance can occur with any non-zero value of a regression coefficient. It depends on the scales of both the predictor and the outcome, of course. But very large samples will confer statistical significance on very small effects.
        Code:
         clear*
        
        . 
        . set seed 1234
        
        . set obs 10000000
        number of observations (_N) was 0, now 10,000,000
        
        . matrix C = (1, 1e-3 \ 1e-3, 1)
        
        . drawnorm x y, corr(C) cstorage(full)
        
        . 
        . regress y x
        
              Source |       SS           df       MS      Number of obs   =  10000000
        -------------+----------------------------------   F(1, 9999998)   =     11.70
               Model |  11.6907384         1  11.6907384   Prob > F        =    0.0006
            Residual |   9993550.8 9,999,998   .99935528   R-squared       =    0.0000
        -------------+----------------------------------   Adj R-squared   =    0.0000
               Total |  9993562.49 9,999,999  .999356349   Root MSE        =    .99968
        
        ------------------------------------------------------------------------------
                   y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
        -------------+----------------------------------------------------------------
                   x |    .001081   .0003161     3.42   0.001     .0004615    .0017004
               _cons |  -.0000271   .0003161    -0.09   0.932    -.0006467    .0005925
        ------------------------------------------------------------------------------

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        • #5
          How is the DV scaled? If your outcome is on a standardized scale then average growth would be zero (average and each time period). Also, if time is measured in months, but the time interest is in academic years/grade levels you would likely be suppressing the values a bit since there are a few months less in an academic year compared to calendar year. It may also be the case that the resolution is too high to identify a more easily interpretable change over time (e.g., a change in IQ by month would probably be very small, while the same change by year may be a bit larger/easier to identify and communicate).

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          • #6
            Originally posted by Jill Fitzgerald View Post
            We do already have the time variable in months (moving from spring of first grade to spring of eighth grade).
            I would measure time in years, i.e. gen time2 = time/12 The variable time2 is measured in years, but no information is lost.
            ---------------------------------
            Maarten L. Buis
            University of Konstanz
            Department of history and sociology
            box 40
            78457 Konstanz
            Germany
            http://www.maartenbuis.nl
            ---------------------------------

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            • #7
              Thank you!!

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