Instrumentation & Measurement Magazine 24-6 - 31

independent measures from Model D. We expected that if the
objective independent measures significantly explained the
engagement scores, the AIC, BIC, and -2 RE/ML log-likelihood
statistics should worsen (i.e., higher values in Model E
in comparison to Model D). The data analyses were all performed
using SPSS 26 (SPSS Inc., Chicago, IL). The p-value was
set at 0.05, two-tailed.
Eq. (2) shows the general specification of the MLMM used
in this study. It represents a longitudinal two-level dataset,
with the first index t being used to indicate a time point, and
the second index i being used for subjects:
Y  
 
i
  Z  ti
01 2i
i Zti
  
12
 
ti
qi Z Random (2)
 
ti
q

lon)
indexes the ni
In this model, the value of t (t = 1, . . . , ni
gitudinal observations of the dependent variable for a given
subject, and i (i = 1, . . ., m) indicates the i-th subject. A two-level
MLMM involves two sets of covariates, namely the X covariates
(i.e., the X(1)
, . . . , X(p)
effects β1, . . . , βp), and the Z covariates (i.e., the Z(1)
variates associated with the random effects φ1i
co,
. . . , φqi
specific
to subject i). Each β parameter represents the fixed effect of a
ti  p X Fixed

01 2
 
12
X Xti

ti
 
 
ti
p

one-unit change in the corresponding X covariate on the mean
value of the dependent variable Y. β0
represents the fixed effect
associated with the intercept, i.e., the grand mean of the
dependent variable when all the covariates are zero. The term
φ0i
in (2) is a vector of the ni
residuals
and represents the variability (σ2
ε) in measuring the individual-level
(i-th subject) outcome on each occasion t.
Results
covariates associated with the fixed
, . . . , Z(q)
Descriptive Statistics
Overall, the engagement and the PANAS scores had a mean
value of 26.68 (SD=4.05) and 24.83 (SD=10.86), respectively.
The high mean value of the engagement scores indicates that
participants' engagement was high. In other words, participants
were in " Flow " while playing the games. The positive
mean value of the PANAS scores indicates that, overall, participants
experienced a more positive affect than a negative affect
while playing the games.
Fig. 2 shows the observed mean engagement scores plotted
against the session numbers for all participants in different
invariant covariates at Level 2 (between groups). The plots
of the mean engagement scores show substantial variations
represents the random effect associated with the intercept of
the i-th subject. The term εti
Fig. 2. Observed mean engagement scores plotted against the session numbers for all participants in different (between) groups. (a) Disturbances; (b) Previous
experience playing mobile games; (c) Cognitive impairment; (d) Game.
September 2021
IEEE Instrumentation & Measurement Magazine
31
Instrumentation & Measurement Magazine 24-6

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