1 ################################### 1  #####################################
   2 ## load the data neighborhood.tab using the read.table() command
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  14 ## Estimate a linear model on attainment (attain) without
  15 ## covariates (null-model), parameter estimates and standard
  16 ## errors; interpret the parameter estimates
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  22 ## Define a second model, allow for the school random effect (schid).
  23 require(lme4)
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  30 ##  What does the output mean? How do you get the corresponding
  31 ## parameter to the estimate from the model without random effect?
  32 ## Do they differ? Why or why not?
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  35 ## visualize the attainment score in different scores using
  36 ## an appropriate plot.  
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  38 require(ggplot2)
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  45 ## Add the observed student specific effects
  46 ## (gender, verbal reasoning quotient, reading ability).
  47 ## How does the magnitude of the school random effect change?
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  49 ## recoding male
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  58 ## use neighid instaed of schid and repeat the analysis
  59 ## add also the deprivation as covariate.
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  66 ## What do the results of using e schid or the neighid
  67 ## random effects tell you about what effects are needed in the
  68 ## modelling of attainment with this data set? ()
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  71 ############################# 2 ############################################
  72 ## load the data
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  76 ## how many observations? 
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  79 ## how many persons?
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  82 ## How many rows per person?
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  85 ## what is the percentage of black?
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  88 ## what the percentage of Hispanic?
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  91 ## what is the percentage of married?
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  95 ## Estimate a logit (binary) model using glm() for trade union
  96 ## membership (union), without covariates, obtain parameter
  97 ## estimates and standard errors.
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 101 invlogit <- function(x){ exp(x)/(exp(x) + 1)}
 102 invlogit(coef(m2.1))
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 105 ## now use the glmer() function (which is the generalized form
 106 ## of the lmer() and add the person identifier as random effect.
 107 ## How does the estimate change?  Is this random effect
 108 ## significant? (use confint())
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 116 ## add lwage as a covariate. interpret the coefficients.
 117