Quantitative data analysis procedures 75

The  quantitative  study  starts  by  describing  the  sample,  with  the  mean,  standard   deviation  and  range  of  different  components  of  the  HLLE  (such  as  the  expectations  of   the  parents  of  the  child’s  schooling  and  the  beliefs  they  held  in  relation  to  language  and   literacy  development,  the  number  of  children’s  books  in  the  home,  frequency  of  shared   book  reading,  other  print  matter  shared  with  the  child,  frequency  of  letter  and  word   identification  activities  at  home  and  time  watching  TV).  The  frequencies  of  these   variables  are  then  compared  to  the  results  obtained  by  other  Chilean  and  international   studies  that  have  analysed  the  same  or  similar  components.    

Following   the   descriptive   analyses,   exploratory   factor   analyses   and   correlations   were   then   used   to   provide   a   preliminary   idea   of   which   variables,   combined   in   which   composites  should  be  included  in  a  predictive  model  of  the  HLLE  for  Chilean  low  SES   families.    

Factor  analyses  have  been  amply  and  successfully  used  in  previous  study  for  example   to  determine  if  different  subsets  of  literacy  skills  represent  the  same  underlying  ability   (Lonigan,  Burguess  &  Anthony,  2000)  and  to  see  if  different  measures  of  oral  language   grouped  together  (Senechal  et  al.,  1998).  

In  order  to  do  the  factor  analyses,  variables  from  the  family  questionnaire  were   grouped  according  to  their  theme  and  four  theoretical  scales  were  built  with  related   variables.  The  first  one  included  variables  on  the  language  and  literacy  resources   available  in  these  low  SES  homes.  The  second  group  included  variables  related  to   language  and  literacy  beliefs  and  expectations.  The  third  group  included  variables   which  assessed  the  frequency  and  variety  of  child  reading,  writing  and  decoding   experiences  in  the  home.  Finally  the  fourth  group  included  items  which  measured  the   frequency  of  decontextualized  conversations  in  the  home.    

Four  separate  factor  analyses  were  then  conducted,  one  on  each  of  the  four  groups.  The   second,  third  and  fourth  groups  of  variables  mentioned  above  included  between  10  and   13  variables.  Through  the  use  of  principal  axis  factoring,  the  exploratory  factor  analysis   permitted  the  selection  of  the  least  factors  that  could  account  for  the  common  variance.   The   factor   analyses   thus   served   to   reduce   the   number   of   variables,   which   was   necessary  to  obtain  a  certain  degree  of  parsimony  in  the  HLLE  model.    

The  exploratory  factor  analyses  were  performed  using  the  Mplus  6.11  program.  More   than  5%  of  data  was  missing  for  each  variable  so  missing  data  treatment  was  used.   Mplus  treats  missing  data  by  analysing  the  frequency  of  the  missing  data  patterns,  after   which  it  imputes  data  for  the  missing  data  and  then  checks  that  the  assumptions  are   met.  Since  the  assumption  of  normal  distribution  was  not  met  for  many  of  the  variables,   the  MLR  estimator  was  used  because  it  was  considered  the  most  robust  estimator  to   deal  with  violation  of  the  assumption  of  multivariate  normality.  Varimax  rotation  was   used  because  as  argued  by  Cohen,  Manion  &  Morrison  (2007)  this  type  of  rotation   allows  for  a  clearer  interpretation  of  the  data,  where  factors  are  more  clearly   distinguished  from  each  other.    

The  dichotomous  variables  within  each  of  the  theoretical  dimensions  were  excluded   from  the  factor  analysis.  Since  Mplus  does  not  calculate  Cronbach´s  Alpha,  it  was  

calculated  manually  with  the  data  from  the  correlation  matrix  using  the  following   formula:  

𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠  𝑎𝑣𝑒𝑟𝑎𝑔𝑒 ∗ 𝑁°  𝑖𝑡𝑒𝑚𝑠 𝑁°  𝑖𝑡𝑒𝑚𝑠 − 1 ∗ (𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠  𝑎𝑣𝑒𝑟𝑎𝑔𝑒 + 1)  

The   rotated   factor   loadings   are   thus   presented   as   well   as   the   composites   that   were   created  with  the  resulting  items.  

Then,  correlational  analyses  looked  at  the  relationship  between  background  variables   (such  as  SES  or  family  demographics)  and  the  development  of  language  and  literacy   skills  as  well  as  the  relationships  between  caregivers´  expectations,  language  and   literacy  beliefs  and  home  literacy  resources  and  the  four  outcome  variables  

(vocabulary,  letter-­‐word  identification,  spelling  and  text  comprehension).  Correlational   analyses  have  been  used  in  previous  HLE  studies  such  as  the  one  by  Leseman  &  de  Jong   (1998)  as  a  preliminary  step  to  path  analyses  and  to  improve  the  understanding  of  the   relationship  between  background  characteristics  and  home  literacy  practices  and   between  home  literacy  practices  and  language  and  literacy  skills.    The  present  research   however  goes  a  step  beyond  by  also  including  correlations  between  these  components   and  caregivers´  language  and  literacy  beliefs.    

Taking  into  consideration  the  results  of  these  analyses,  a  hypothetical  model  of  the   HLLE  of  Chilean  low  SES  urban  families  with  preschoolers  was  developed  and  is   presented.  As  a  first  step,  four  separate  path  analyses  models  were  tested,  one  for  each   of  the  four  outcomes.  These  models  were  then  compared  and  their  fit  indices  discussed.   The  fit  of  the  path  models  for  each  individual  outcome  supported  the  plausibility  of  an   overall  model  with  all  four  outcomes.  This  “overall”  model  includes  distal  and  proximal   components  and  presents  a  hypothesis  of  their  direct  or  mediated  influence  on  the  four   language  outcomes  as  measured  by  some  tests  of  the  Woodcock  Muñoz  Language   Survey  revised  (WMLS-­‐R).  The  results  of  this  overall  model,  and  of  the  four  individual   models  are  compared  and  commented.    

Path  analysis  had  several  features  that  fit  well  with  the  specific  purposes  and  holistic   perspective  of  the  current  HLLE  research  such  as  a)  the  flexibility  regarding  the  types   of  relationships  that  can  be  specified  in  the  hypothetical  model,  b)  the  comprehensive   view  it  provided  of  the  relationship  between  distal  and  proximal  variables,  or  c)  the  fact   that  it  allowed  for  several  outcome  variables  to  be  included  simultaneously.  Section  III   in  chapter  IV  provides  a  more  detailed  explanation  of  the  advantages  of  path  analysis   over  other  types  of  regression  analysis  in  relation  to  the  purposes  of  this  research.    

This  research  was  informed  by  the  experience  of  previous  studies  that  explored  the   Home  Learning  Environment  using  path  analysis.  For  example,  Leseman  &  de  Jong,   (1998)  used  path  analysis  to  assess  “the  relationships  between  sociocultural  and  ethnic-­‐ cultural  background,  home  literacy,  home  language,  and  early  language  and  literacy   learning  in  school”  (p.311).  

In  a  similar  fashion  to  Leseman  &  de  Jong´s  study,  in  the  present  research  background   characteristics  were  considered  exogenous  variables  that  predicted  home  literacy  and   language  practices.  

Leseman  &  de  Jong´s  conceptualization  of  home  literacy  included  measures  of   frequency  of  literacy-­‐related  interactions  in  the  home,  but  also  included  measures  of   the  quality  of  these  interactions.  Similar  measures  of  the  quality  of  interactions  were   unfortunately  not  available  in  the  UBC  parent  questionnaire.    

Leseman  &  de  Jong´s  conceptualization  of  home  literacy  was  mostly  focused  on  shared   reading.  However,  since  there  is  evidence  that  shared  reading  is  not  a  frequent  practice   in  Chilean  homes,  for  the  purpose  of  the  present  research  it  seemed  more  valid  to   include  measures  of  word  and  letter  writing  and  identification  in  addition  to  the   measures  of  the  frequency  of  shared  reading  in  the  path  model  because  there  is   evidence  that  these  practices  happen  more  frequently  in  Chilean  homes.  

When  analysing  their  sample  that  included  different  ethnic  subgroups  Leseman  and  de   Jong  discovered  that  background  characteristics  of  the  families  were  strongly  

associated  to  home  literacy  practices  and  to  language  and  literacy  measures.     Considering  that  the  present  research  analyses  represents  a  seemingly  more   homogeneous  sample  of  mid  to  low  SES  Chilean  families,  it  seemed  interesting  to   investigate  if  minor  variations  in  background  characteristics,  such  as  SES,  would  still  be   strongly  associated  with  home  literacy  practices  and  language  and  literacy  measures.    

Finally,  the  home  literacy  opportunity  facet  included  in  Leseman  &  de  Jong´s  study  was   based  on  self-­‐reports  and  measured  by  a  questionnaire.  Even  though  they  

acknowledged  the  desirability  bias  that  this  might  have  implied,  they  argued  that  none   of  the  analyses  indicated  that  such  an  effect  was  present.  This  supported  the  use  of  data   from  a  questionnaire  for  the  present  research.  

Path  analysis  is  usually  considered  a  confirmatory  rather  than  exploratory  type  of   statistical  analysis.  However,  several  studies  using  path  analyses  models  test  the  fit  of   their  model,  then  modify  it  (by  deleting  or  adding  parameters)  and  retest  the  new  

model.  For  example,  Farver  et  al.  (2006)  used  a  path  analysis  to  first  assess  the  fit  of  a   model  that  assessed  the  relations  between      “parents’  literacy  involvement,  mothers’   parenting  stress,  and  children’s  PPVT-­‐R/TVIP  scores  and  social  functioning,  without   considering  the  children’s  literacy  interest”  and  then  entered  another  HLLE  scale   (parents’  reports  of  children’s  literacy  interest)  to  test  how  much  it  mediated  between   parents  literacy  involvement  and  children´s  school  readiness  outcomes.  Then  they   dropped  some  of  the  non-­‐significant  associations  that  emerged  and  produced  an   overall  model  with  acceptable  fit.  

However,  as  reviewed  by  Hox  &  Bechger  (1998,  p.  9-­‐10)  there  is  evidence  that  “model   modification  often  fails  to  find  the  correct  model  (Spirtes,  Scheines  &  Glymour,  1991),  and   that  models  so  achieved  cross-­‐validate  badly  (Maccallum,  1986;  MacCallum,  Roznowskei   &  Necowitz,  1992)”.    

One  alternative  way  of  testing  the  stability  of  the  present  research´s  model  would  have   been  to  divide  the  sample  in  two  groups,  test  a  path  analysis  model  on  a  first  group,   modify  it  until  the  fit  indices  were  acceptable  and  then  cross  validate  the  model  with   the  second  group.    

However,  in  the  view  of  this  researcher,  path  analysis  is  more  a  model  testing,  rather   than  model  producing  procedure,  i.e.  it  is  a  procedure  where  a  model  based  on  theory   and  knowledge  of  a  specific  set  of  variables  and  populations  is  tested.  Consequently,  a   more  confirmatory  rather  than  exploratory  approach  to  path  analyses  was  taken  in  this   research.  

After  the  path  analysis  was  conducted,  a  direct  discriminant  analysis  was  performed   using  the  scales  from  the  path  analysis  model  as  predictors  and  a  composite  of  the   results  of  the  four  outcome  tests  as  a  dependent  variable.  The  main  purpose  of  the   discriminant  analysis  was  to  build  an  index  to  help  categorize  the  families  according  to   the  quality  of  HLLE  provided.  As  a  result,  the  homes  in  the  sample  were  then  classified   into  three  groups:  high  HLLE,  medium  HLLE  and  low  HLLE.  A  subsample  from  each  of   these  three  groups  is  used  for  the  qualitative  study.