Dissertation Analyses

load(file="/Users/meganwilliams/Desktop/Dissertation/StroopMixed.rdata")
load(file="/Users/meganwilliams/Desktop/Dissertation/Allvars.rdata")
library(effects)
library(interactions)

Stroop Color-Word Test - Psychological Aggression

Model 1

SCWTlog1 <- glm(PsychAggress ~ StroopMixed, data=StroopMixed,family = "binomial")
summary(SCWTlog1)
## 
## Call:
## glm(formula = PsychAggress ~ StroopMixed, family = "binomial", 
##     data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3248   0.4332   0.5120   0.5923   0.8944  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  0.55268    0.38541   1.434  0.15157   
## StroopMixed  0.03925    0.01221   3.213  0.00131 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 452.04  on 547  degrees of freedom
## Residual deviance: 441.36  on 546  degrees of freedom
## AIC: 445.36
## 
## Number of Fisher Scoring iterations: 4
confint(SCWTlog1)
##                   2.5 %     97.5 %
## (Intercept) -0.19647466 1.31824277
## StroopMixed  0.01558201 0.06356161
exp(cbind(OR = coef(SCWTlog1), confint(SCWTlog1)))
##                   OR     2.5 %   97.5 %
## (Intercept) 1.737909 0.8216221 3.736849
## StroopMixed 1.040030 1.0157040 1.065625
plot(predictorEffect("StroopMixed",SCWTlog1))

########Compare to null model 
#Difference in Deviance
with(SCWTlog1,null.deviance - deviance)
## [1] 10.68401
#Degrees of freedom for the difference between two models
with(SCWTlog1,df.null - df.residual)
## [1] 1
#p-value
with(SCWTlog1,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))
## [1] 0.001080657

Model 2

SCWTlog2 <- glm(PsychAggress ~ StroopMixed + Age + Sex + PovStat + WRATtotal, data = StroopMixed, family = "binomial")
summary(SCWTlog2)
## 
## Call:
## glm(formula = PsychAggress ~ StroopMixed + Age + Sex + PovStat + 
##     WRATtotal, family = "binomial", data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3956   0.4030   0.5069   0.5948   0.9438  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   0.99698    1.12674   0.885   0.3762  
## StroopMixed   0.02973    0.01419   2.095   0.0361 *
## Age          -0.01789    0.01502  -1.191   0.2338  
## SexMen       -0.32165    0.24818  -1.296   0.1950  
## PovStatBelow  0.28470    0.28846   0.987   0.3237  
## WRATtotal     0.01800    0.01818   0.990   0.3222  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 452.04  on 547  degrees of freedom
## Residual deviance: 435.89  on 542  degrees of freedom
## AIC: 447.89
## 
## Number of Fisher Scoring iterations: 5
confint(SCWTlog2)
##                     2.5 %     97.5 %
## (Intercept)  -1.202319724 3.22403985
## StroopMixed   0.002045792 0.05778365
## Age          -0.047571215 0.01146232
## SexMen       -0.811751656 0.16397948
## PovStatBelow -0.267438077 0.86796109
## WRATtotal    -0.018211855 0.05328156
exp(cbind(OR = coef(SCWTlog2), confint(SCWTlog2)))
##                     OR     2.5 %    97.5 %
## (Intercept)  2.7100891 0.3004963 25.129435
## StroopMixed  1.0301771 1.0020479  1.059486
## Age          0.9822704 0.9535426  1.011528
## SexMen       0.7249506 0.4440795  1.178190
## PovStatBelow 1.3293567 0.7653377  2.382049
## WRATtotal    1.0181610 0.9819530  1.054727
plot(allEffects(SCWTlog2))

########Compare to null model 
#Difference in Deviance
with(SCWTlog2,null.deviance - deviance)
## [1] 16.1543
#Degrees of freedom for the difference between two models
with(SCWTlog2,df.null - df.residual)
## [1] 5
#p-value
with(SCWTlog2,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))
## [1] 0.006417072

Model 3

SCWTlog3 <- glm(PsychAggress ~ (StroopMixed + Sex + PovStat)^3 + Age + WRATtotal, data = StroopMixed, family = "binomial")
summary(SCWTlog3)
## 
## Call:
## glm(formula = PsychAggress ~ (StroopMixed + Sex + PovStat)^3 + 
##     Age + WRATtotal, family = "binomial", data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3828   0.3929   0.5067   0.6024   0.9833  
## 
## Coefficients:
##                                 Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                      0.51878    1.25468   0.413   0.6793  
## StroopMixed                      0.04568    0.02265   2.016   0.0438 *
## SexMen                           0.36679    0.92214   0.398   0.6908  
## PovStatBelow                     0.47415    1.32994   0.357   0.7215  
## Age                             -0.01746    0.01506  -1.159   0.2463  
## WRATtotal                        0.01894    0.01836   1.032   0.3022  
## StroopMixed:SexMen              -0.02635    0.02888  -0.912   0.3615  
## StroopMixed:PovStatBelow        -0.01309    0.04323  -0.303   0.7621  
## SexMen:PovStatBelow             -0.12800    1.76637  -0.072   0.9422  
## StroopMixed:SexMen:PovStatBelow  0.01670    0.05833   0.286   0.7747  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 452.04  on 547  degrees of freedom
## Residual deviance: 434.45  on 538  degrees of freedom
## AIC: 454.45
## 
## Number of Fisher Scoring iterations: 5
confint(SCWTlog3)
##                                        2.5 %     97.5 %
## (Intercept)                     -1.933308023 2.99882242
## StroopMixed                      0.002187172 0.09153845
## SexMen                          -1.446357087 2.18326044
## PovStatBelow                    -2.110003807 3.15042319
## Age                             -0.047217545 0.01196513
## WRATtotal                       -0.017581384 0.05460431
## StroopMixed:SexMen              -0.083643507 0.02999360
## StroopMixed:PovStatBelow        -0.096984597 0.07394836
## SexMen:PovStatBelow             -3.603769499 3.36101186
## StroopMixed:SexMen:PovStatBelow -0.098817961 0.13091968
exp(cbind(OR = coef(SCWTlog3), confint(SCWTlog3)))
##                                        OR      2.5 %    97.5 %
## (Intercept)                     1.6799779 0.14466884 20.061899
## StroopMixed                     1.0467372 1.00218957  1.095859
## SexMen                          1.4430962 0.23542637  8.875196
## PovStatBelow                    1.6066418 0.12123750 23.345942
## Age                             0.9826880 0.95387986  1.012037
## WRATtotal                       1.0191218 0.98257227  1.056123
## StroopMixed:SexMen              0.9739945 0.91975909  1.030448
## StroopMixed:PovStatBelow        0.9869981 0.90756999  1.076751
## SexMen:PovStatBelow             0.8798572 0.02722092 28.818336
## StroopMixed:SexMen:PovStatBelow 1.0168376 0.90590760  1.139876
plot(predictorEffect("StroopMixed",SCWTlog3))

########Compare to null model 
#Difference in Deviance
with(SCWTlog3,null.deviance - deviance)
## [1] 17.58857
#Degrees of freedom for the difference between two models
with(SCWTlog3,df.null - df.residual)
## [1] 9
#p-value
with(SCWTlog3,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))
## [1] 0.04025829

Compare Models 1,2, & 3

anova(SCWTlog1,SCWTlog2,test = "LR")
## Analysis of Deviance Table
## 
## Model 1: PsychAggress ~ StroopMixed
## Model 2: PsychAggress ~ StroopMixed + Age + Sex + PovStat + WRATtotal
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1       546     441.36                     
## 2       542     435.89  4   5.4703   0.2424
anova(SCWTlog2,SCWTlog3,test = "LR")
## Analysis of Deviance Table
## 
## Model 1: PsychAggress ~ StroopMixed + Age + Sex + PovStat + WRATtotal
## Model 2: PsychAggress ~ (StroopMixed + Sex + PovStat)^3 + Age + WRATtotal
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1       542     435.89                     
## 2       538     434.45  4   1.4343   0.8382
anova(SCWTlog1,SCWTlog3,test = "LR")
## Analysis of Deviance Table
## 
## Model 1: PsychAggress ~ StroopMixed
## Model 2: PsychAggress ~ (StroopMixed + Sex + PovStat)^3 + Age + WRATtotal
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1       546     441.36                     
## 2       538     434.45  8   6.9046    0.547

Suggested Model by Predictors

anova(SCWTlog3, test="Chisq")
## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: PsychAggress
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                                      547     452.04            
## StroopMixed              1  10.6840       546     441.36 0.001081 **
## Sex                      1   1.8894       545     439.47 0.169269   
## PovStat                  1   1.3364       544     438.13 0.247664   
## Age                      1   1.2788       543     436.85 0.258129   
## WRATtotal                1   0.9657       542     435.89 0.325757   
## StroopMixed:Sex          1   0.9346       541     434.95 0.333666   
## StroopMixed:PovStat      1   0.0253       540     434.93 0.873703   
## Sex:PovStat              1   0.3926       539     434.53 0.530935   
## StroopMixed:Sex:PovStat  1   0.0818       538     434.45 0.774897   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
SCWTlog4 <- glm(PsychAggress ~ StroopMixed, data = StroopMixed, family = "binomial")
summary(SCWTlog4)
## 
## Call:
## glm(formula = PsychAggress ~ StroopMixed, family = "binomial", 
##     data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3248   0.4332   0.5120   0.5923   0.8944  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  0.55268    0.38541   1.434  0.15157   
## StroopMixed  0.03925    0.01221   3.213  0.00131 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 452.04  on 547  degrees of freedom
## Residual deviance: 441.36  on 546  degrees of freedom
## AIC: 445.36
## 
## Number of Fisher Scoring iterations: 4
plot(allEffects(SCWTlog4))

Stroop Color-Word Test - Physical Assault

Model 1

SCWTlog1 <- glm(PhysAssault ~ StroopMixed, data=StroopMixed,family = "binomial")
summary(SCWTlog1)
## 
## Call:
## glm(formula = PhysAssault ~ StroopMixed, family = "binomial", 
##     data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.5817  -0.5063  -0.4888  -0.4695   2.1974  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -2.39524    0.45602  -5.252  1.5e-07 ***
## StroopMixed  0.01067    0.01296   0.823     0.41    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 391.02  on 547  degrees of freedom
## Residual deviance: 390.34  on 546  degrees of freedom
## AIC: 394.34
## 
## Number of Fisher Scoring iterations: 4
confint(SCWTlog1)
##                   2.5 %      97.5 %
## (Intercept) -3.31626204 -1.52583659
## StroopMixed -0.01475071  0.03614618
exp(cbind(OR = coef(SCWTlog1), confint(SCWTlog1)))
##                     OR      2.5 %    97.5 %
## (Intercept) 0.09115035 0.03628822 0.2174391
## StroopMixed 1.01072943 0.98535755 1.0368074
########Compare to null model 
#Difference in Deviance
with(SCWTlog1,null.deviance - deviance)
## [1] 0.678027
#Degrees of freedom for the difference between two models
with(SCWTlog1,df.null - df.residual)
## [1] 1
#p-value
with(SCWTlog1,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))
## [1] 0.4102669

Model 2

SCWTlog2 <- glm(PhysAssault ~ StroopMixed + Age + Sex + PovStat + WRATtotal, data = StroopMixed, family = "binomial")
summary(SCWTlog2)
## 
## Call:
## glm(formula = PhysAssault ~ StroopMixed + Age + Sex + PovStat + 
##     WRATtotal, family = "binomial", data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.8575  -0.5252  -0.4387  -0.3595   2.4818  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  -1.923475   1.308109  -1.470   0.1414  
## StroopMixed  -0.002239   0.015751  -0.142   0.8870  
## Age          -0.030718   0.016570  -1.854   0.0638 .
## SexMen       -0.340829   0.279464  -1.220   0.2226  
## PovStatBelow  0.670720   0.289539   2.317   0.0205 *
## WRATtotal     0.028233   0.022555   1.252   0.2107  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 391.02  on 547  degrees of freedom
## Residual deviance: 376.77  on 542  degrees of freedom
## AIC: 388.77
## 
## Number of Fisher Scoring iterations: 5
confint(SCWTlog2)
##                    2.5 %      97.5 %
## (Intercept)  -4.52828769 0.613429348
## StroopMixed  -0.03313450 0.028730582
## Age          -0.06373628 0.001399406
## SexMen       -0.89963957 0.200617507
## PovStatBelow  0.09865659 1.237696041
## WRATtotal    -0.01471822 0.073934791
exp(cbind(OR = coef(SCWTlog2), confint(SCWTlog2)))
##                     OR      2.5 %   97.5 %
## (Intercept)  0.1460984 0.01079915 1.846754
## StroopMixed  0.9977633 0.96740843 1.029147
## Age          0.9697488 0.93825241 1.001400
## SexMen       0.7111802 0.40671622 1.222157
## PovStatBelow 1.9556456 1.10368721 3.447661
## WRATtotal    1.0286353 0.98538956 1.076737
########Compare to null model 
#Difference in Deviance
with(SCWTlog2,null.deviance - deviance)
## [1] 14.24441
#Degrees of freedom for the difference between two models
with(SCWTlog2,df.null - df.residual)
## [1] 5
#p-value
with(SCWTlog2,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))
## [1] 0.01412921

Model 3

SCWTlog3 <- glm(PhysAssault ~ (StroopMixed + Sex + PovStat)^3 + Age + WRATtotal, data = StroopMixed, family = "binomial")
summary(SCWTlog3)
## 
## Call:
## glm(formula = PhysAssault ~ (StroopMixed + Sex + PovStat)^3 + 
##     Age + WRATtotal, family = "binomial", data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.8174  -0.5564  -0.4236  -0.3232   2.5111  
## 
## Coefficients:
##                                 Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                     -2.78652    1.43745  -1.939   0.0526 .
## StroopMixed                      0.02099    0.02257   0.930   0.3524  
## SexMen                           1.84015    1.24297   1.480   0.1388  
## PovStatBelow                     1.24604    1.35126   0.922   0.3565  
## Age                             -0.02924    0.01667  -1.754   0.0794 .
## WRATtotal                        0.02940    0.02237   1.314   0.1888  
## StroopMixed:SexMen              -0.07248    0.03617  -2.004   0.0451 *
## StroopMixed:PovStatBelow        -0.02215    0.03823  -0.579   0.5623  
## SexMen:PovStatBelow             -2.03683    1.95253  -1.043   0.2969  
## StroopMixed:SexMen:PovStatBelow  0.07915    0.05825   1.359   0.1742  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 391.02  on 547  degrees of freedom
## Residual deviance: 371.47  on 538  degrees of freedom
## AIC: 391.47
## 
## Number of Fisher Scoring iterations: 5
confint(SCWTlog3)
##                                       2.5 %       97.5 %
## (Intercept)                     -5.66663487 -0.016991478
## StroopMixed                     -0.02299517  0.065885642
## SexMen                          -0.63428162  4.271705151
## PovStatBelow                    -1.46094828  3.874539036
## Age                             -0.06242361  0.003099514
## WRATtotal                       -0.01319397  0.074756970
## StroopMixed:SexMen              -0.14463657 -0.002266140
## StroopMixed:PovStatBelow        -0.09735843  0.053418320
## SexMen:PovStatBelow             -5.89405066  1.798465502
## StroopMixed:SexMen:PovStatBelow -0.03451700  0.194549935
exp(cbind(OR = coef(SCWTlog3), confint(SCWTlog3)))
##                                         OR       2.5 %     97.5 %
## (Intercept)                     0.06163505 0.003459487  0.9831521
## StroopMixed                     1.02121051 0.977267205  1.0681046
## SexMen                          6.29748378 0.530316321 71.6436948
## PovStatBelow                    3.47654803 0.232016154 48.1604929
## Age                             0.97118439 0.939484830  1.0031043
## WRATtotal                       1.02983659 0.986892686  1.0776222
## StroopMixed:SexMen              0.93008782 0.865336727  0.9977364
## StroopMixed:PovStatBelow        0.97809470 0.907230769  1.0548708
## SexMen:PovStatBelow             0.13044162 0.002755791  6.0403714
## StroopMixed:SexMen:PovStatBelow 1.08236894 0.966071912  1.2147641
interact_plot(model = SCWTlog3, pred = StroopMixed, modx = Sex)

sim_slopes(SCWTlog3, pred = StroopMixed, modx = Sex, centered = "all",jnplot = TRUE)
## Warning: Johnson-Neyman intervals are not available for factor moderators.
## SIMPLE SLOPES ANALYSIS 
## 
## Slope of StroopMixed when Sex = Men: 
## 
##    Est.   S.E.   z val.      p
## ------- ------ -------- ------
##   -0.03   0.02    -1.42   0.16
## 
## Slope of StroopMixed when Sex = Women: 
## 
##   Est.   S.E.   z val.      p
## ------ ------ -------- ------
##   0.01   0.02     0.74   0.46
########Compare to null model 
#Difference in Deviance
with(SCWTlog3,null.deviance - deviance)
## [1] 19.55291
#Degrees of freedom for the difference between two models
with(SCWTlog3,df.null - df.residual)
## [1] 9
#p-value
with(SCWTlog3,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))
## [1] 0.02088115

Compare Models 1,2, & 3

anova(SCWTlog1,SCWTlog2,test = "LR")
## Analysis of Deviance Table
## 
## Model 1: PhysAssault ~ StroopMixed
## Model 2: PhysAssault ~ StroopMixed + Age + Sex + PovStat + WRATtotal
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)   
## 1       546     390.34                        
## 2       542     376.77  4   13.566 0.008816 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(SCWTlog2,SCWTlog3,test = "LR")
## Analysis of Deviance Table
## 
## Model 1: PhysAssault ~ StroopMixed + Age + Sex + PovStat + WRATtotal
## Model 2: PhysAssault ~ (StroopMixed + Sex + PovStat)^3 + Age + WRATtotal
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1       542     376.77                     
## 2       538     371.47  4   5.3085   0.2571
anova(SCWTlog1,SCWTlog3,test = "LR")
## Analysis of Deviance Table
## 
## Model 1: PhysAssault ~ StroopMixed
## Model 2: PhysAssault ~ (StroopMixed + Sex + PovStat)^3 + Age + WRATtotal
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       546     390.34                       
## 2       538     371.47  8   18.875  0.01554 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Suggested Model by Predictors

anova(SCWTlog3, test="Chisq")
## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: PhysAssault
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                                      547     391.02            
## StroopMixed              1   0.6780       546     390.34 0.410267   
## Sex                      1   1.9635       545     388.38 0.161145   
## PovStat                  1   6.8160       544     381.56 0.009034 **
## Age                      1   3.1583       543     378.40 0.075543 . 
## WRATtotal                1   1.6286       542     376.77 0.201893   
## StroopMixed:Sex          1   2.6238       541     374.15 0.105273   
## StroopMixed:PovStat      1   0.0702       540     374.08 0.791079   
## Sex:PovStat              1   0.7544       539     373.33 0.385085   
## StroopMixed:Sex:PovStat  1   1.8601       538     371.47 0.172609   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
SCWTlog4 <- glm(PhysAssault ~ PovStat + Age, data = StroopMixed, family = "binomial")
summary(SCWTlog4)
## 
## Call:
## glm(formula = PhysAssault ~ PovStat + Age, family = "binomial", 
##     data = StroopMixed)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.7410  -0.5281  -0.4482  -0.3757   2.3858  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  -0.75584    0.72639  -1.041   0.2981  
## PovStatBelow  0.59571    0.27780   2.144   0.0320 *
## Age          -0.03296    0.01544  -2.134   0.0328 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 391.02  on 547  degrees of freedom
## Residual deviance: 379.98  on 545  degrees of freedom
## AIC: 385.98
## 
## Number of Fisher Scoring iterations: 5