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I am having difficulties in interpreting my R output for a multilevel model I have conducted using the NLME package. I'm looking to answer the following questions:

1) What are the predictors of curiosity scores at each given timepoint. 2) Are there significant individual differences in curiosity scores over time?

How is it best to write these results up? I understand the intercept score but struggling to establish if any predictors significantly predict curiosity scores across each timepoint.

For example: I have used a random intercept and random slope model as it is the best fitting according to LogLik. The intercept value for Mod1 is 3.57. The value for wellbeing is 0.22. Does this value represent the estimated score for curiosity at T0 only or does it represent the score at each given timepoint. For every 1 increase on curiosity, wellbeing increases by 0.22 at each timepoint.

Mod1: has continuous predictors only

Mod2: has categorical (binary (Yes/No) answers

For Mod2: Being bored is a significant predictor - does this represent the score at T0 only (i.e. if one is bored at T0, their curiosity score is 0.29 lower. OR does it mean that at each timepoint, bored people have a score 0.29 lower in curiosity. What do the interaction scores tell us?

Thank you for any help given. If anyone has any recommendations of books with examples, please let me know!

I have read a number of chapters including Singer (2003) and Hoffman (2007) but to no avail. I am looking to understand the intra and inter-individual differences of my data.

#Add predictors (Facets)
Mod1<-lme(Curiosity~Timepoint + Wellbeing + Resiliency + Anxiety +          Timepoint*Wellbeing + Timepoint*Resiliency + Timepoint*Anxiety, random=~Timepoint|PersonalID, correlation=corAR1(), na.action=na.omit, method = "ML", data = Abroad, control=list(opt="optim"))
summary(Mod1)

#Get intervals

intervals(Mod1)

#Get Variance 

VarCorr(Mod1)

#Add predictors (Environmental)
Mod2<-lme(Curiosity~Timepoint + CloseBond + NegativeEvent + Socialised + Bored + ActiveMember + VisitedHome + VisitedCountry + Welcomed + Loneliness + CloseBond*Timepoint + NegativeEvent*Timepoint + Socialised*Timepoint + Bored*Timepoint + ActiveMember*Timepoint + VisitedHome*Timepoint + VisitedCountry*Timepoint + Welcomed*Timepoint + Loneliness*Timepoint, random=~Timepoint|PersonalID, correlation=corAR1(), na.action=na.omit, method = "ML", data = Abroad, control=list(opt="optim"))
 summary(Mod2)
 #Get intervals
 intervals(Mod2)
 #Get variance
 VarCorr(Mod2)

 Linear mixed-effects model fit by maximum likelihood
 Data: Abroad 
 AIC      BIC    logLik
 1047.82 1060.694 -520.9098

 Random effects:
 Formula: ~1 | PersonalID
           (Intercept)  Residual
 StdDev:   0.5952816 0.5141837


 Fixed effects: Curiosity ~ 1 
               Value  Std.Error  DF  t-value p-value
 (Intercept) 3.491608 0.05978863 424 58.39919       0

 Standardized Within-Group Residuals:
           Min          Q1         Med          Q3         Max 
     -3.68499329 -0.58453669  0.05547817  0.58567994  3.16488126 

Number of Observations: 540
Number of Groups: 116 

#Get intervals
intervals(NullModelAb)
Approximate 95% confidence intervals

Fixed effects:
              lower     est.    upper
(Intercept) 3.374197 3.491608 3.609018
attr(,"label")
[1] "Fixed effects:"

Random Effects:
Level: PersonalID 
                  lower      est.     upper
sd((Intercept)) 0.5127646 0.5952816 0.6910777

 Within-group standard error:
  lower      est.     upper 
 0.4807975 0.5141837 0.5498883 

#Get Variance 
VarCorr(NullModelAb)
PersonalID = pdLogChol(1) 
         Variance  StdDev   
(Intercept) 0.3543602 0.5952816
Residual    0.2643849 0.5141837

 #Get ICC
 varests<-as.numeric(VarCorr(NullModelAb)[1:2])
 ICC<-varests[1]/sum(varests)
 ICC
 [1] 0.5727079

 #Add predictors (Facets)
 Mod1<-lme(Curiosity~Timepoint + Wellbeing + Resiliency + Anxiety +   Timepoint*Wellbeing + Timepoint*Resiliency + Timepoint*Anxiety, random=~Timepoint|PersonalID, correlation=corAR1(), na.action=na.omit, method = "ML", data = Abroad, control=list(opt="optim"))
 summary(Mod1)
 Linear mixed-effects model fit by maximum likelihood
 Data: Abroad 
   AIC      BIC  logLik
 873.0601 928.8505 -423.53

 Random effects:
 Formula: ~Timepoint | PersonalID
 Structure: General positive-definite, Log-Cholesky parametrization
               StdDev     Corr  
 (Intercept) 0.46479620 (Intr)
 Timepoint   0.04346893 -0.371
 Residual    0.45997912       

 Correlation Structure: AR(1)
 Formula: ~1 | PersonalID 
 Parameter estimate(s):
 Phi 
 0.2032922 
 Fixed effects: Curiosity ~ Timepoint + Wellbeing + Resiliency + Anxiety + Timepoint *      Wellbeing + Timepoint * Resiliency + Timepoint * Anxiety 
                          Value  Std.Error  DF  t-value p-value
  (Intercept)           3.576185 0.05865561 417 60.96918  0.0000
  Timepoint            -0.043266 0.01572791 417 -2.75092  0.0062
  Wellbeing             0.222911 0.13013084 417  1.71298  0.0875
  Resiliency            0.358679 0.07264770 417  4.93723  0.0000
  Anxiety              -0.061841 0.09076172 417 -0.68135  0.4960
  Timepoint:Wellbeing   0.027132 0.04862147 417  0.55803  0.5771
  Timepoint:Resiliency -0.035262 0.02770357 417 -1.27284  0.2038
  Timepoint:Anxiety    -0.019123 0.03674592 417 -0.52042  0.6031

  Standardized Within-Group Residuals:
       Min          Q1         Med          Q3         Max 
  -3.00135444 -0.51964841  0.07674468  0.56085924  2.73837107 

  Number of Observations: 540
  Number of Groups: 116 

  #Get intervals
  intervals(Mod1)
  Approximate 95% confidence intervals

  Fixed effects:
                            lower        est.       upper
  (Intercept)           3.46174439  3.57618468  3.69062497
  Timepoint            -0.07395230 -0.04326629 -0.01258029
  Wellbeing            -0.03098100  0.22291133  0.47680366
  Resiliency            0.21693896  0.35867857  0.50041819
  Anxiety              -0.23892159 -0.06184054  0.11524050
  Timepoint:Wellbeing  -0.06773081  0.02713231  0.12199543
  Timepoint:Resiliency -0.08931329 -0.03526211  0.01878906
  Timepoint:Anxiety    -0.09081643 -0.01912314  0.05257016
  attr(,"label")
  [1] "Fixed effects:"

  Random Effects:
  Level: PersonalID 
                                 lower        est.     upper
  sd((Intercept))             0.352166426  0.46479620 0.6134472
  sd(Timepoint)               0.002237124  0.04346893 0.8446326
  cor((Intercept),Timepoint) -0.827756828 -0.37119674 0.3811018

  Correlation structure:
        lower      est.     upper
  Phi -0.007890915 0.2032922 0.3971155
  attr(,"label")
  [1] "Correlation structure:"

   Within-group standard error:
   lower      est.     upper 
  0.3978689 0.4599791 0.5317852 

  #Get Variance 
  VarCorr(Mod1)
  PersonalID = pdLogChol(Timepoint) 
                Variance    StdDev     Corr  
  (Intercept) 0.216035511 0.46479620 (Intr)
  Timepoint   0.001889548 0.04346893 -0.371
  Residual    0.211580794 0.45997912       

  #Add predictors (Environmental)
  Mod2<-lme(Curiosity~Timepoint + CloseBond + NegativeEvent + Socialised + Bored + ActiveMember + VisitedHome + VisitedCountry + Welcomed + Loneliness + CloseBond*Timepoint + NegativeEvent*Timepoint + Socialised*Timepoint + Bored*Timepoint + ActiveMember*Timepoint + VisitedHome*Timepoint + VisitedCountry*Timepoint + Welcomed*Timepoint + Loneliness*Timepoint, random=~Timepoint|PersonalID, correlation=corAR1(), na.action=na.omit, method = "ML", data = Abroad, control=list(opt="optim"))
  summary(Mod2)
  Linear mixed-effects model fit by maximum likelihood
  Data: Abroad 
      AIC      BIC    logLik
  799.8266 901.3047 -374.9133

  Random effects:
  Formula: ~Timepoint | PersonalID
  Structure: General positive-definite, Log-Cholesky parametrization
                StdDev    Corr  
  (Intercept) 0.5401980 (Intr)
  Timepoint   0.1299729 -0.436
  Residual    0.4467650       

  Correlation Structure: AR(1)
  Formula: ~1 | PersonalID 
  Parameter estimate(s):
  Phi 
  0.05452504 
  Fixed effects: Curiosity ~ Timepoint + CloseBond + NegativeEvent + Socialised +      Bored + ActiveMember + VisitedHome + VisitedCountry + Welcomed +      Loneliness + CloseBond * Timepoint + NegativeEvent * Timepoint +      Socialised * Timepoint + Bored * Timepoint + ActiveMember *      Timepoint + VisitedHome * Timepoint + VisitedCountry * Timepoint +      Welcomed * Timepoint + Loneliness * Timepoint 
                               Value  Std.Error  DF   t-value p-value
   (Intercept)               4.099345 0.29673249 295 13.814952  0.0000
   Timepoint                -0.231005 0.10190074 295 -2.266964  0.0241
   CloseBond                 0.059946 0.16914646 295  0.354402  0.7233
   NegativeEvent            -0.108776 0.13184714 295 -0.825017  0.4100
   Socialised                0.048427 0.12817812 295  0.377809  0.7058
   Bored                    -0.294181 0.13104608 295 -2.244869  0.0255
   ActiveMember              0.115505 0.14192490 295  0.813846  0.4164
   VisitedHome               0.016310 0.16712510 295  0.097590  0.9223
   VisitedCountry           -0.112230 0.14687423 295 -0.764121  0.4454
   Welcomed                 -0.222340 0.19837259 295 -1.120821  0.2633
   Loneliness               -0.280334 0.14474632 295 -1.936725  0.0537
   Timepoint:CloseBond       0.001579 0.05582692 295  0.028289  0.9775
   Timepoint:NegativeEvent  -0.000847 0.04925498 295 -0.017187  0.9863
   Timepoint:Socialised      0.031332 0.04731939 295  0.662129  0.5084
   Timepoint:Bored           0.054365 0.04777743 295  1.137873  0.2561
   Timepoint:ActiveMember    0.014350 0.05038636 295  0.284790  0.7760
   Timepoint:VisitedHome    -0.060044 0.05407914 295 -1.110298  0.2678
   Timepoint:VisitedCountry  0.072866 0.05269433 295  1.382809  0.1678
   Timepoint:Welcomed        0.164198 0.07023776 295  2.337739  0.0201
   Timepoint:Loneliness     -0.000819 0.05071029 295 -0.016146  0.9871

   Standardized Within-Group Residuals:
       Min          Q1         Med          Q3         Max 
   -2.59823030 -0.51307530  0.01394587  0.56477949  3.02787645 

  Number of Observations: 428
  Number of Groups: 114 

  #Get intervals
  intervals(Mod2)
  Approximate 95% confidence intervals

  Fixed effects:
                              lower          est.        upper
  (Intercept)               3.52917202  4.0993452263  4.669518432
  Timepoint                -0.42680813 -0.2310052660 -0.035202407
  CloseBond                -0.26507006  0.0599458430  0.384961748
  NegativeEvent            -0.36212113 -0.1087760873  0.144568953
  Socialised               -0.19786813  0.0484268717  0.294721874
  Bored                    -0.54598706 -0.2941812585 -0.042375460
  ActiveMember             -0.15720456  0.1155049655  0.388214487
  VisitedHome              -0.30482206  0.0163098020  0.337441660
  VisitedCountry           -0.39444942 -0.1122297323  0.169989954
  Welcomed                 -0.60351418 -0.2223400998  0.158833979
  Loneliness               -0.55846477 -0.2803338686 -0.002202971
  Timepoint:CloseBond      -0.10569248  0.0015792832  0.108851041
  Timepoint:NegativeEvent  -0.09549028 -0.0008465407  0.093797196
  Timepoint:Socialised     -0.05959292  0.0313315565  0.122256033
  Timepoint:Bored          -0.03743994  0.0543646730  0.146169287
  Timepoint:ActiveMember   -0.08246813  0.0143495545  0.111167241
  Timepoint:VisitedHome    -0.16395733 -0.0600439566  0.043869421
  Timepoint:VisitedCountry -0.02838629  0.0728661776  0.174118648
  Timepoint:Welcomed        0.02923525  0.1641975113  0.299159771
  Timepoint:Loneliness     -0.09825890 -0.0008187795  0.096621339
  attr(,"label")
  [1] "Fixed effects:"

  Random Effects:
  Level: PersonalID 
                                 lower       est.     upper
  sd((Intercept))             0.35216010  0.5401980 0.8286398
  sd(Timepoint)               0.06611156  0.1299729 0.2555218
  cor((Intercept),Timepoint) -0.78006403 -0.4356044 0.1114830

  Correlation structure:
        lower       est.     upper
  Phi -0.28255 0.05452504 0.3796148
  attr(,"label")
  [1] "Correlation structure:"

  Within-group standard error:
    lower      est.     upper 
  0.3610882 0.4467650 0.5527707 

 #Get variance
 VarCorr(Mod2)
 PersonalID = pdLogChol(Timepoint) 
               Variance   StdDev    Corr  
 (Intercept) 0.29181388 0.5401980 (Intr)
 Timepoint   0.01689294 0.1299729 -0.436
 Residual    0.19959899 0.4467650
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closed as too broad by Michael Chernick, Peter Flom Aug 23 at 10:35

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