2 edited title

1

# Orders of variables in nested models (in R)

I am trying to use nested models to investigate the influence of 5 factors on my dependent variable. I am not interested in interactions, only the influence of each variable taken separately. My dependent variable is part4Auto, and my independent variables are:

• part1FlyingHours
• part1TypePilot
• part3SUS
• part5MWQ

So I wrote this nested model sequence which gave me the following output:

> model.baseline = lm(part4Auto ~ 1, data)
> model.1 = update(model.baseline, .~. + part1FlyingHours)
> model.2 = update(model.1, .~. + part1TypePilot)
> model.3 = update(model.2, .~. + part3SUS)
> model.4 = update(model.3, .~. + part5MWQ)
> anova(model.baseline, model.1, model.2, model.3, model.4)

Analysis of Variance Table
Model 1: part4Auto ~ 1
Model 2: part4Auto ~ part1FlyingHours
Model 3: part4Auto ~ part1FlyingHours + part1TypePilot
Model 4: part4Auto ~ part1FlyingHours + part1TypePilot + part3SUS
Model 5: part4Auto ~ part1FlyingHours + part1TypePilot + part3SUS + part5MWQ
Res.Df    RSS Df Sum of Sq       F    Pr(>F)
1     41 22.562
2     40 21.578  1    0.9846  3.2352  0.080460 .
3     38 19.665  2    1.9125  3.1419  0.055249 .
4     37 13.418  1    6.2477 20.5279 6.241e-05 ***
5     36 10.957  1    2.4612  8.0866  0.007306 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


The problem is that when I change the order of independent variables, I obtain different results which almost modify my conclusion (here I exchanged part1FlyingHours and part5MWQ):

> model.baseline = lm(part4Auto ~ 1, data)
> model.1 = update(model.baseline, .~. + part5MWQ)
> model.2 = update(model.1, .~. + part1TypePilot)
> model.3 = update(model.2, .~. + part3SUS)
> model.4 = update(model.3, .~. + part1FlyingHours)
> anova(model.baseline, model.1, model.2, model.3, model.4)

Analysis of Variance Table
Model 1: part4Auto ~ 1
Model 2: part4Auto ~ part5MWQ
Model 3: part4Auto ~ part5MWQ + part1TypePilot
Model 4: part4Auto ~ part5MWQ + part1TypePilot + part3SUS
Model 5: part4Auto ~ part5MWQ + part1TypePilot + part3SUS + part1FlyingHours
Res.Df    RSS Df Sum of Sq       F    Pr(>F)
1     41 22.562
2     40 15.226  1    7.3367 24.1063 1.979e-05 ***
3     38 14.680  2    0.5462  0.8973  0.416588
4     37 10.978  1    3.7015 12.1619  0.001304 **
5     36 10.957  1    0.0215  0.0707  0.791882
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


On the contrary, the output given by summary() does not change.

So my question is: for nested models, does the order of introduction of variables change the results so much? Or do I have an important flaw (like unbalanced data)? And if it is the first solution, what can I do to ensure that my results are not biased or incomplete?