Step 1: Estimate the null model

Using SPSS Mixed

SPSS menus

We find the Mixed procedure under Analyze in the menu:

Figure 4.4.

This opens the Linear Mixed Models dialogue box, where Subjects (level 2 unit identifier) have to be defined as shown here:

Figure 4.5.

Next, press Continue and define the dependent variable as shown. In the null model, we do not need any factors (categorical explanatory variables) or covariates (continuous explanatory variables).

Figure 4.6.

Next, press Random and define Combinations as firmno.

Figure 4.7.

Press Continue and then Estimation to change from default to ML estimation. In addition, the default settings for the estimation procedures can be changed here:

Figure 4.8.

Press Continue and then Statistics to define the output to be printed. The minimum option is to select Parameters estimates:

Figure 4.9.

SPSS syntax

Pressing Paste produces the syntax below. The lines with criteria are only necessary if the default values for the estimation procedure need to be changed.

MIXED wage
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=| SSTYPE(3)
/METHOD=ML
/PRINT=SOLUTION
/RANDOM=INTERCEPT | SUBJECT(firmno) COVTYPE(VC)
/EMMEANS=TABLES(OVERALL).

Table 4.1. Estimates of Fixed Effectsa

Table 4.2. Estimates of Covariance Parametersa

Stata xtmixed

The following one-line command will suffice:

. xtmixed wage || firmno: , ml variance

Stata output

Table 4.3

Note that the Stata output also includes a Likelihood ratio (LR) test, where the current model is compared to the linear regression model. The probability value indicates that the random intercepts represent a significant improvement compared with the OLS model. Also note that ‘variance’ is added to the command to produce an estimate of the random terms as variances rather than as standard deviations.

Question (both Stata and SPSS)

Calculate and interpret the intraclass correlation (ICC). Does the result indicate that a two-level model is required?

Answer

ICC = 0.288

Interpretation:
About 29 per cent of the variance in wages stems from differences among firms. This clearly indicates that a multilevel model is required.

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