title: dredge in MuMin (R) keeps models with higher order terms without their respective lower order terms
body: <p>I am using the function dredge from package MuMin for model selection. My model has a polynomial in it. I was under the impression (<a href="https://www.rdocumentation.org/packages/MuMIn/versions/1.42.1/topics/dredge" rel="nofollow noreferrer">https://www.rdocumentation.org/packages/MuMIn/versions/1.42.1/topics/dredge</a>, see "Interactions") that MuMin as standard ditches models that include the higher order term without its respective lower order term; however when I use it the top model includes only the higher order term. </p>
  
  <p>Here is the code I am using to make the global model, which includes <code>hour</code>: at both first and second order</p>
  
  <pre><code>sc.mod.env.hour&lt;-clmm(seedcat~hour+I(hour^2)+MeanSpeed+RH+TKE+AirTemp+MeanUpdraft+(1|jdayfac), data=sc.data, na.action = na.fail, Hess =TRUE)
  </code></pre>
  
  <p>However when I run dredge:</p>
  
  <pre><code>dro.env.hour&lt;-dredge(sc.mod.env.hour)
  </code></pre>
  
  <p>The output includes models that include <code>I(hour^2)</code> without <code>hour</code></p>
  
  <pre><code>Model selection table 
      (Intrc)   ArTmp    hour hour^2 MnSpd    MnUpd     RH      TKE df   logLik   AICc  delta weight
  46        + -1.2170         -3.340 1.894          -4.219          13 -571.772 1170.5   0.00  0.154
  62        + -1.3410         -3.478 1.964  0.30990 -4.269          14 -570.882 1170.9   0.37  0.128
  45        +                 -2.882 2.052          -3.214          12 -573.245 1171.3   0.81  0.103
  47        +         -0.3595 -2.670 1.942          -3.601          13 -572.374 1171.7   1.20  0.084
  63        +         -0.4495 -2.712 2.010  0.33870 -3.645          14 -571.350 1171.8   1.30  0.080
  </code></pre>
  
  <p>I have tried also using <code>poly(hour,2)</code> to define the global model but this results in only including a single term for hour. </p>
  
  <p>I am using <code>clmm</code> but have tried a simpler model using <code>lm</code> and got the same result. </p>
  
  <p>Any guidance appreciated thankyou. I wasn't sure if this should be on crossvalidated but it is a programming issue rather than a stats issue so thought it should be here. </p>
  
  <p>EDIT: I have solved the issue by using subset:</p>
  
  <pre><code>dro.env.hour&lt;-dredge(sc.mod.env.hour, subset=(dc(hour, I(hour^2)))
  </code></pre>
  
  <p>Although it is not clear why this is an issue in the first place. </p>