Analisis Multilevel Modeling Melalui Program SPSS

Two-Level School Effects  Models

MIXED mathach

/print=solution G TESTCOV

/random intercept | subject(school).

In this  case,  we  find that the  estimated  value  of 700 = 8.6096  and  the  estimated  value  of a2  = 39.1487. These  estimates   suggest  that  schools  do  differ in  their average MATHACH scores  and that there is even more variation among students within schools.   (The  variance  component within school is  nearly five  times  the size  of the  variance  component between schools).

Including EffectsofSchoolLevel(level2)Predictors

The  two terms in the first bracket represents  the fixed part, consisting of the two gamma  terms.  The  two terms  in the  second bracket represent the  random part, consisting of the  u0j (which  represents  variation in intercepts  between schools) and the  rij  (which  represents  variation within  schools).

Estimated  Fixed Effects

Fixed effects information. The term for the INTERCEPT, 12.65, estimates gamma-00, the school mean math achievement when the remaining predictors (here, just MEANSES) are 0. Because MEANSES is centered at the grand mean (with a mean of 0), gamma-00 is the estimated MATHACH in a school of  "average MEANSES."

The term for MEANSES, 5.86, provides our estimate of the other fixed effect, gamma-01, and tells us about the relationship between math achievement and MEANSES. Schools that differ by 1 point in MEANSES differ by 5.86 points in MATHACH. Its standard error of 0.36 yields an observed r-statistic of 16.22 (p<.0001), which indicates that we reject the null hypothesis that there is no relationship between a school ' s SES and the math achievement scores of its students.

Covariance parameter estimates

These tell us about the random effects. We now estimate tau-00 to be 2.65 and sigma-2 to be 39.16. Although we have used the same symbols in models (3) and (5) to represent these variance components, note that they have very different meanings. In the previous model , there were no predictors, so these were unconditional components. Having added a predictor, these are now conditional components. Notice that the conditional component for the variance within school (the residual component representing a 2 ) has remained virtually unchanged (going from 39.15 to 39.16) . The variance component representing variation between schools, however, has diminished markedly (go- ing from 8.61 to 2.64). This tells us that the predictor MEAN SES explains a large portion of the school-to-school variation in mean math achievement .

Including Effects of Student-Level(level-1)Predictors

mixed mathach with cses

/print=solution G TESTCOV

/fixed = cses

/random intercept cses | subject(school) covtype(un).

Including Both  Level-1 and Level-2 Predictors

Syntax SPSS

mixed mathach with meanses sector cses

/print=solution G TESTCOV

/fixed = meanses sector cses meanses*cses sector*cses

Hasil Analisis SPSS

Tabel di bawah ini menunjukkan bahwa SES secara umum mempengaruhi kemampuan matematika siswa, meskipun jenis sekolah (SECTOR) telah dikendalikan. Terlihat pada variabel MEANSES, SECTOR, dan CSES memiliki nilai estimasi dengan nilai p (sig) di bawah 0.01.

Persamaan regresi yang didapatkan dari hasil di atas adalah seperti yang tertulis di bawah ini. Persamaan tersebut didapatkan dari tabel di atas.

-    Kemampuan Matematika Sekolah Publik :

MATHACH = 12.11 + 5.34 MEANSES  + 2.94 CSES + 1.03 MEANSES*CSES

-    Kemampuan Matematika Sekolah Privat :

MATHACH = 13.33 + 5.34 MEANSES + 1.30 CSES + 1.03  MEANSES*CSES

Nilai 13.33 pada kemampuan matematika sekolah privat didapatkan dari penambahan nilai estimasi dari intercept dengan nilai SECTOR (12.11 + 1.22).

Tabel di bawah ini menunjukkan :

1.       UN (2,2) menunjukkan perbedaan slope. Nilai 0.101 (p=0.635) menujukkan bahwa perbedaan kemiringan garis antar sekolah tidak berbeda secara signifikan.

2.       UN (2,1) menunjukkan hubungan antara intercept dan slope. Nilai 0.192 (p=0.635) menunjukkan bahwa tidak ada hubungan yang signifikan.