dsM <- dplyr::filter(dsL, id == 1) %>% 
  dplyr::select(id, year, attend, attendF)
dsM

   id year attend         attendF
1   1 2000      1           Never
2   1 2001      6 About once/week
3   1 2002      2   Once or Twice
4   1 2003      1           Never
5   1 2004      1           Never
6   1 2005      1           Never
7   1 2006      1           Never
8   1 2007      1           Never
9   1 2008      1           Never
10  1 2009      1           Never
11  1 2010      1           Never
12  1 2011      1           Never

How often did you attend a worhsip service during the last year?

  attendLevels         attendLabels
1            8             Everyday
2            7   Several times/week
3            6      About once/week
4            5    About twice/month
5            4     About once/month
6            3 Less than once/month
7            2        Once or Twice
8            1                Never

• what criteria used?
• not used?
• preferences in fit/parsimony
• complex judgments

Challenges:

1. Collecting results
   • What pieces of information do we need?
     
2. Organizing comparisons
   • How do we overcome information overload?

Model A: \({y_{it}} = {\beta _0} + {\varepsilon _{it}}\)

Model B: \({y_{it}} = {\beta _0} + {\beta _1}tim{e_t} + {\varepsilon _{it}}\)

print(mA)

         modelA
logLik    -3727
deviance   7453
AIC        7457
BIC        7468
df.resid   1859
N          1860
p             1
ids         155

modelA

Generalized least squares fit by REML
  Model: attend ~ 1 
  Data: dsM 
  Log-restricted-likelihood: -3727

Coefficients:
(Intercept) 
      2.477 

Degrees of freedom: 1860 total; 1859 residual
Residual standard error: 1.793 

\({y_{it}} = {\beta _0} + {\varepsilon _{it}}\)

print(mB)

         modelB
logLik    -3719
deviance   7438
AIC        7444
BIC        7461
df.resid   1858
N          1860
p             2
ids         155

modelB

Generalized least squares fit by REML
  Model: attend ~ 1 + time 
  Data: dsM 
  Log-restricted-likelihood: -3719

Coefficients:
(Intercept)        time 
     2.7882     -0.0566 

Degrees of freedom: 1860 total; 1858 residual
Residual standard error: 1.782 

\({y_{it}} = {\beta _0} + {\beta _1}tim{e_t} + {\varepsilon _{it}}\)