Interpreting significance - HLM using REML and Kenward-Roger-corr.

Dear Statalisters,

I struggle with interpreting my results from multilevel linear regressions, using restricted maximum likelihood and Kenward-Roger correction. I use Stata 15.0 on a Mac (version 10.14), and I hope I’m using the Code-function right.

My problem is that I do not know how to interpret the significance of the coefficients in my multilevel outputs. I’m doing my master thesis, so I will report significance at both the 0.1-, 0.05-, 0.01- and 0.001-level in my regression tables.

For example, from reading off P>|t| in the output below, I immediately thought that x1-x3 are statistically significant (x1 at the 0.1-level, x2 at the 0.01-level, x3 at the 0.001-level). However, is that the correct interpretation? The confusion arise as I do not know how to calculate the critical t-value, so that I can compare t from the output to the critical t-value. I tried using this calculatur (http://www.ttable.org/student-t-value-calculator.html), plotting in df=6, but I'm not sure this yields the right value. The critical value for a two-tail test with significance level 0.01 is calculated to be +/-3.71. However, if x2 is significant at the 0.01-level (which I though from reading its P>|t|), why is the t-value only 3.43, which yields a significance at the 0.05-level if the critical t-value is 3.71? Is the critical t-value in fact something else, or is my interpretation of P>|t| wrong?

Code:

mixed CHILDREN x1 x2 x3 || COUNTRY2:, reml dfmethod(kroger)

Code:

Mixed-effects REML regression                   Number of obs     =      3,245
Group variable: COUNTRY2                        Number of groups  =         10

                                                Obs per group:
                                                              min =        108
                                                              avg =      324.5
                                                              max =        466
DF method: Kenward-Roger                        DF:           min =      16.07
                                                              avg =   1,561.11
                                                              max =   3,240.03

                                                F(3,    98.23)    =      21.91
Log restricted-likelihood = -4836.0572          Prob > F          =     0.0000

--------------------------------------------------------------------------------
      CHILDREN |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
x1 |   .2339834   .1167206     2.00   0.058    -.0091296    .4770963
x2 |    .133747   .0389608     3.43   0.001     .0573566    .2101373
x3 |   .0837528   .0124587     6.72   0.000     .0593243    .1081814
_cons |   .5332078   .2389675     2.23   0.040     .0268024    1.039613
--------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
COUNTRY2: Identity           |
                  var(_cons) |   .1383108   .0711551      .0504601    .3791085
-----------------------------+------------------------------------------------
               var(Residual) |   1.136198   .0282628      1.082133    1.192965
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 124.99        Prob >= chibar2 = 0.0000

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |        Obs  ll(null)  ll(model)      df         AIC        BIC
-------------+---------------------------------------------------------------
           . |      3,245         .  -4836.057       6    9684.114   9720.624
-----------------------------------------------------------------------------

All help is very much appreciated.


Kind regards,

Frøydis Jensen