# Interpreting nested mixed effects modelling output

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?

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)

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
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

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
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

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
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


## migrated from stackoverflow.comAug 23 at 0:00

This question came from our site for professional and enthusiast programmers.