title: p-values of linear combination of coefficients in linear mixed model
body: <p>I fitted a linear mixed model using lme function of nlme package in R.
  My goal is to find a p-value of a linear combination of coefficients of fixed effects part.</p>
  
  <pre><code>                 Value   Std.Error    DF   t-value p-value
  (Intercept) -1.5897634 0.019578359 41547 -81.20004  0.0000
  group_k      0.0866493 0.027662455   594   3.13238  0.0018
  x1           0.1621744 0.006963385 41547  23.28960  0.0000
  </code></pre>
  
  <p>For example, p-value of the hypothesis $ \beta_1 = 0 $ is provided in this result (0.0018).
  But if I want to find a p-value of a hypothesis such as $ \beta_1 + 3 * \beta_2 = $, what should I do?
  Is there any ready-made command to do this calculation?</p>