###############Comparing  models ###########

###Man in the Middle Data, Overall Rating#########
> M.model = lmer(OverallRating ~   Network + Transaction+ Password +Timer + (1 | ID), data=Mdata, REML=FALSE)
> M.null = lmer(OverallRating ~   1 + (1 | ID), data=Mdata, REML=FALSE)
>  anova(M.model, M.null)
Data: Mdata
Models:
M.null: OverallRating ~ 1 + (1 | ID)
M.model: OverallRating ~ Network + Transaction + Password + Timer + (1 | 
M.model:     ID)
        Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)    
M.null   3 1154.1 1167.7 -574.04   1148.1                             
M.model  9 1023.9 1064.7 -502.95   1005.9 142.18      6  < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

###Packet Sniffing Data, Overall Rating#########

> P.model = lmer(OverallRating ~   Network + Transaction+ Password +Timer + (1 | ID), data=Pdata, REML=FALSE)
> P.null = lmer(OverallRating ~   1 + (1 | ID), data=Pdata, REML=FALSE)
>  anova(P.model, P.null)
Data: Pdata
Models:
P.null: OverallRating ~ 1 + (1 | ID)
P.model: OverallRating ~ Network + Transaction + Password + Timer + (1 | 
P.model:     ID)
        Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)   
P.null   3 50.713 61.733 -22.357   44.713                            
P.model  9 42.892 75.951 -12.446   24.892 19.822      6   0.002979 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Pinter.model = lmer(OverallRating ~   Network + Transaction+ Password +Timer + Network*Transaction + Network*Password + Network*Timer + Transaction*Password + Transaction*Timer + Password*Timer + (1 | ID), data=Pdata, REML=FALSE)
fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
> 
> anova(P.model, Pinter.model)
Data: Pdata
Models:
P.model: OverallRating ~ Network + Transaction + Password + Timer + (1 | 
P.model:     ID)
Pinter.model: OverallRating ~ Network + Transaction + Password + Timer + Network * 
Pinter.model:     Transaction + Network * Password + Network * Timer + Transaction * 
Pinter.model:     Password + Transaction * Timer + Password * Timer + (1 | 
Pinter.model:     ID)
             Df    AIC     BIC   logLik deviance  Chisq Chi Df Pr(>Chisq)
P.model       9 42.892  75.951 -12.4458   24.892                         
Pinter.model 20 57.136 130.603  -8.5682   17.136 7.7551     11     0.7351
> 

##################################

Extracting the OverallRating Coefficients: 
#####The Man in the Middle Data##########
display(M.model)
lmer(formula = OverallRating ~ Network + Timer + Password + Transaction + 
    (1 | ID), data = Mdata)
                      coef.est coef.se
(Intercept)           -0.23     0.07  
NetworkPublicWIFI     -0.50     0.05  
NetworkVPNEncrypted    0.03     0.05  
NetworkVPNUnencrypted -0.24     0.05  
Timeryes               0.13     0.08  
Passwordweak           0.05     0.07  
TransactionF          -0.04     0.06  

Error terms:
 Groups   Name        Std.Dev.
 ID       (Intercept) 0.31    
 Residual             0.44    
---
number of obs: 687, groups: ID, 174
AIC = 1056.7, DIC = 979.4
deviance = 1009.1 
#############Showing coefficients and p-values ####################
> coefs$p.z <- 2 * (1 - pnorm(abs(coefs$t.value)))
> coefs
                         Estimate Std..Error     t.value          p.z
(Intercept)           -0.22917274 0.07111609  -3.2225161 1.270700e-03
NetworkPublicWIFI     -0.49629280 0.04796519 -10.3469372 0.000000e+00
NetworkVPNEncrypted    0.03256336 0.04785024   0.6805266 4.961711e-01
NetworkVPNUnencrypted -0.23564014 0.04779790  -4.9299265 8.226057e-07
Timeryes               0.12773518 0.07915010   1.6138347 1.065633e-01
Passwordweak           0.05152638 0.06964482   0.7398451 4.593940e-01
TransactionF          -0.03798549 0.05798512  -0.6550902 5.124097e-01