When searching for correlations between between a dependent variable and a factor or a combination of factors in a repeated measure design with lme() I noticed that I can encounter two types of results, and I am wondering which is the best way to report each of them in a journal publication. It is not clear to me when I should report the values of the beta coefficient together with the t-test value and p-value, or the beta coefficient with F value and p-value.
Let’s have as a reference the following two models:
MODEL TYPE 1: fixed effects only
lme_Weigth <- lme(Sound_Feature ~ Weight, data = My_Data, random = ~1 | Subject)
summary(lme_Weigth)
lme_Height <- lme(Sound_Feature ~ Height, data = My_Data, random = ~1 | Subject)
summary(lme_Height)
MODEL TYPE 2: Fixed and interaction effects together
lme_Interaction <- lme(Sound_Feature ~ Weight*Height, data = My_Data, random = ~1 | Subject)
summary(lme_Interaction)
anova.lme(lme_Interaction, type = "marginal").
RESULTS CASE 1: Applying model type 2 I do not get any significant p-value so there is no interaction effect. Therefore I check the simplified model type 1, and I get for both Height and Weight significant p-values.
RESULTS CASE 2: Applying model type 2 I get a significant p-value so there is an interaction effect. Therefore I do not check the simplified model type 1 for the two factors separately. Moreover, in the results of model type 2 I can also see that the fixed effects of both factors are significant.
I am not sure if in presence of an interaction it is correct to report the significant interactions of the separate factors, since I read somewhere that it does not make too much sense. Am I wrong?
My attempt in reporting the results for the two cases is the following. Can you please tell me it I am right?
“We performed a linear mixed effects analysis of the relationship between Sound_Feature and Height and Weight. As fixed effects, we entered Height and Weight (without interaction term) into a first model, and we included the interaction effect into a second model. As random effects, we had intercepts for subjects.”
RESULTS CASE 1: “Results showed that Sound_Feature was linearly related to Height (beta = value, t(df)= value, p < 0.05) and Weight (beta = value, t(df)= value, p < 0.05), but no to their interaction effect.”
RESULTS CASE 2: “Results showed that Sound_Feature was linearly related to Height (beta = value, F(df)= value, p < 0.05) and Weight (beta = value, F(df)= value, p < 0.05), and to their interaction effect (beta = value, F(df)= value, p < 0.05).”
Basically I used for reporting the beta value in the 2 cases I use the output of summary(). In the case 1, I report the value of the t-test, still taken from summary. But for case 2 I do not report the t-test, I report the F value as result of anova.lme(lme_Interaction, type = "marginal").
Is this the correct way of proceeding in the results reporting?
I give an example of the outputs I get using the two models for the three cases:
RESULTS CASE 1:
> ############### Sound_Level_Peak vs Weight*Height ###############
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>
>
> library(nlme)
> lme_Sound_Level_Peak <- lme(Sound_Level_Peak ~ Weight*Height, data = My_Data1, random = ~1 | Subject)
>
> summary(lme_Sound_Level_Peak)
Linear mixed-effects model fit by REML
Data: My_Data1
AIC BIC logLik
716.2123 732.4152 -352.1061
Random effects:
Formula: ~1 | Subject
(Intercept) Residual
StdDev: 5.470027 4.246533
Fixed effects: Sound_Level_Peak ~ Weight * Height
Value Std.Error DF t-value p-value
(Intercept) -7.185833 97.56924 95 -0.0736485 0.9414
Weight 0.993543 1.63151 15 0.6089715 0.5517
Height -0.076300 0.55955 15 -0.1363592 0.8934
Weight:Height -0.005403 0.00898 15 -0.6017421 0.5563
Correlation:
(Intr) Weight Height
Weight -0.927
Height -0.994 0.886
Weight:Height 0.951 -0.996 -0.919
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.95289464 -0.51041805 -0.06414148 0.48562230 2.95415889
Number of Observations: 114
Number of Groups: 19
> anova.lme(lme_Sound_Level_Peak,type = "marginal")
numDF denDF F-value p-value
(Intercept) 1 95 0.0054241 0.9414
Weight 1 15 0.3708463 0.5517
Height 1 15 0.0185938 0.8934
Weight:Height 1 15 0.3620936 0.5563
>
>
> ############### Sound_Level_Peak vs Weight ###############
>
> library(nlme)
> summary(lme(Sound_Level_Peak ~ Weight, data = My_Data1, random = ~1 | Subject))
Linear mixed-effects model fit by REML
Data: My_Data1
AIC BIC logLik
706.8101 717.6841 -349.4051
Random effects:
Formula: ~1 | Subject
(Intercept) Residual
StdDev: 5.717712 4.246533
Fixed effects: Sound_Level_Peak ~ Weight
Value Std.Error DF t-value p-value
(Intercept) -3.393843 6.291036 95 -0.5394728 0.5908
Weight -0.196214 0.087647 17 -2.2386822 0.0388
Correlation:
(Intr)
Weight -0.976
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.90606493 -0.51419643 -0.05659565 0.56770327 3.00098859
Number of Observations: 114
Number of Groups: 19
>
>
>
>
>
>
> ############### Sound_Level_Peak vs Height ###############
>
> library(nlme)
> summary(lme(Sound_Level_Peak ~ Height, data = My_Data1, random = ~1 | Subject))
Linear mixed-effects model fit by REML
Data: My_Data1
AIC BIC logLik
702.9241 713.7981 -347.462
Random effects:
Formula: ~1 | Subject
(Intercept) Residual
StdDev: 5.174077 4.246533
Fixed effects: Sound_Level_Peak ~ Height
Value Std.Error DF t-value p-value
(Intercept) 46.36896 20.764187 95 2.233122 0.0279
Height -0.36643 0.119588 17 -3.064113 0.0070
Correlation:
(Intr)
Height -0.998
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.93697776 -0.50963502 -0.06774953 0.50428597 2.97007576
Number of Observations: 114
Number of Groups: 19
>
>
So, I will report the results in this way: “Results showed that Sound_Level_Peak was linearly related to Height (beta = -0.36643, t(17)= -3.064113, p = 0.007) and Weight (beta = -0.196214, t(17)= -2.2386822, p < 0.0388), but no to their interaction effect.”
RESULTS CASE 2:
> ############### Centroid vs Weight*Height ###############
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>
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> library(nlme)
> lme_Centroid <- lme(Centroid ~ Weight*Height, data = My_Data2, random = ~1 | Subject)
>
> summary(lme_Centroid)
Linear mixed-effects model fit by REML
Data: My_Data2
AIC BIC logLik
1904.563 1920.766 -946.2817
Random effects:
Formula: ~1 | Subject
(Intercept) Residual
StdDev: 1180.301 945.3498
Fixed effects: Centroid ~ Weight * Height
Value Std.Error DF t-value p-value
(Intercept) -45019.39 21114.912 95 -2.132113 0.0356
Weight 710.53 353.074 15 2.012414 0.0625
Height 330.61 121.092 15 2.730246 0.0155
Weight:Height -4.34 1.943 15 -2.233779 0.0411
Correlation:
(Intr) Weight Height
Weight -0.927
Height -0.994 0.886
Weight:Height 0.951 -0.996 -0.919
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.16255520 -0.60084449 -0.02651629 0.54377042 1.92638924
Number of Observations: 114
Number of Groups: 19
> anova.lme(lme_Centroid,type = "marginal")
numDF denDF F-value p-value
(Intercept) 1 95 4.545908 0.0356
Weight 1 15 4.049810 0.0625
Height 1 15 7.454243 0.0155
Weight:Height 1 15 4.989769 0.0411
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>
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So, I will report the results in this way: “Results showed that Centroid was linearly related to the interaction effect of Weight and Height (beta = -4.34, F(1,15)= 4.989769, p = 0.0411), and to Height (beta = 330.61, F(1,15)= 7.454243, p = 0.0155).
