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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 ###############
> 
>
> 
> 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 ###############
> 
> 
> 
> 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
> 
> 
> 

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).

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