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I have data structured in a long format which contains repeated values for every participant v001. I run a mixed models analysis with random coefficients to investigate the relationship between my dependent variable ln_slope, which is an index measure for bronchial hyperreactivity, and some predictors. I want to investigate if changes in ln_slope depend on some factors. I calculated time for every individual starting from baseline (0).

The data looks like the:

structure(list(v001 = c(10002, 10002, 10002, 10002, 10002, 10004, 
10004, 10004, 10005, 10005, 10005, 10006, 10006, 10006, 10006, 
10006, 10006, 10006, 10007, 10007), time = c(0, 3, 6, 9, 12, 
0, 3, 6, 0, 6, 9, 0, 3, 9, 12, 15, 18, 21, 0, 3), age = c(46.4394250513347, 
49.4565366187543, 52.4462696783025, 55.4496919917864, 58.444900752909, 
22.9158110882957, 25.9247091033539, 28.9199178644764, 15.3182751540041, 
21.3169062286105, 24.3066392881588, 14.8856947296372, 17.8809034907598, 
23.8795345653662, 26.8939082819986, 29.8726899383984, 32.8843258042437, 
35.8740588637919, 27.4579055441478, 30.466803559206), bmi = c(27.6094517551723, 
29.7520661157025, 29.3946871824648, 30.119375573921, 29.3946871824648, 
25.3902185223725, 26.4855397496689, 25.7210322145387, 18.8323917137476, 
21.6788067984738, 22.2569083130998, 20.8979591836735, 23.7196092506476, 
23.2005432322318, 25.207756232687, 27.4445450430059, 27.1669192713546, 
27.7488727020465, 23.6202879121581, 22.8571428571429), ln_slope = c(0.0507723253734231, 
0.606135803570316, 0.192160005794242, 0.10951852580649, 0.374693449441411, 
NA, 0.218445030532656, NA, 0.313091787977149, NA, -0.0361572285993463, 
0.800960043896479, NA, NA, NA, 1.37147927533475, 1.53234783071453, 
0.996237878364571, -0.133531392624523, -0.0408887702539783), 
    sexe = structure(c(2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("female", 
    "male"), class = "factor"), bronch = structure(c(2L, 2L, 
    2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 
    1L, 2L, 2L), .Label = c("yes", "no"), class = "factor")), .Names = c("v001", 
"time", "age", "bmi", "ln_slope", "sexe", "bronch"), row.names = c(5L, 
6L, 7L, 8L, 9L, 12L, 13L, 14L, 20L, 22L, 23L, 29L, 30L, 32L, 
33L, 34L, 35L, 36L, 41L, 42L), class = "data.frame")

And the model I run was:

model.1=lme(ln_slope~time+sexe*time+age*time+bmi*time+bronch*time,random=~1|v001,data=gaga,na.action="na.omit") 

My questions are:

  1. How can I interpret the interactions with time for variables such as BMI and categorical ones such as bronch? Considering that my dependent variable is also a changing variable.

  2. What does the coefficient for time indicate?

  3. What is the difference between the coefficients between, say, bronchno and time:bronchno?

Here is the output: (bronchno is the estimate for people who said no when asked if they have bronchitis, the reference group is bronchyes - those who said yes)

                   Value    Std.Error   DF    t-value      p-value
(Intercept)   -0.1405926367 1.017008e-01 4312 -1.3824144 1.669161e-01
time           0.0081936566 8.151101e-03 4312  1.0052208 3.148470e-01
sexemale      -0.0040153945 2.743607e-02 1490 -0.1463546 8.836613e-01
age            0.0054305993 1.224855e-03 4312  4.4336684 9.494741e-06
bmi            0.0129494923 3.772421e-03 4312  3.4326738 6.032847e-04
bronchno      -0.0395274443 3.429395e-02 4312 -1.1526069 2.491357e-01
time:sexemale  0.0033349796 1.936829e-03 4312  1.7218765 8.516362e-02
time:age       0.0002534342 8.304164e-05 4312  3.0518934 2.287877e-03
time:bmi      -0.0001388647 2.758376e-04 4312 -0.5034291 6.146883e-01
time:bronchno -0.0053347104 3.243086e-03 4312 -1.6449490 1.000532e-01
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I've generally been advised to run a main effects-only model before running a model with interaction effects. The latter can be tricky to interpret. But, to your questions. Let's assume that time is coded in months (and you had measures at baseline, then 3, 6, 9, and 12 months).

2) The average change in log-hyperreactivity (in females, age 0, with bronchitis) is 0.00819 units per month. But remember, you logged your DV.

3) The coefficient for no bronchitis (that's the variable bronchno) means this: those without bronchitis had baseline log-hyperreactivity measures 0.0395 less than those with.

1) For bronchitis: those without bronchitis have an growth rate in log-hyperreactivity of 0.0053 units less than those with.

It's a bit harder to comprehend continuous-continuous interactions, but the explanation is similar. Here, each unit of BMI was associated with a 0.0129 unit increase in log-hyperreactivity at baseline, but a lower growth rate in log-hyperreactivity.

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