Calculating estimates

Initial estimates are obtained by the PROX algorithm, and then more refined ones by the JMLE (UCON) algorithm. Check that convergence is occurring by reviewing the "Residual" and "Change" columns for smaller values each iteration. The iterative process can be terminated by pressing Ctrl+S simultaneously.

With T3onscreen= No, so that detailed output is displayed:

Table 3. Iteration Report

Iteration 1 Largest Residuals |----------Score------------| logit Measure

Facet Name No./Cat Raw Expected Residual Resd% Value Change

>=============================================================================<

Junior Sc Betty 2 79 .740 .740

Iteration 1 PROX max.= .740

PROX - "normal approximation algorithm" is used to make initial estimates.

If "PROX Recount required" is displayed, some elements or categories had a 0 or perfect score. Measure for these can not be estimated directly, so their estimation is deferred and all marginal scores recounted without them. PROX ceases when the maximum change is less than 0.1 logits

Iteration 2 Largest Residuals |----------Score------------| logit Measure

Facet Name No./Cat Raw Expected Residual Resd% Value Change

Checking subset connection..

>=============================================================================<

Scale: ?B,?B,?,CREATIVI 4 31 6.3 24.7 79.8 -.948 -.948

Scale: ?B,?B,?,CREATIVI 5 6 6.5 -.5 -8.7 .961 .961

Junior Sc Fred 6 39 18.0 21.0 17.5 -.409 .237

Iteration 2 JMLE max.= 21.0 17.5 max.= .237

JMLE= "joint maximum likelihood estimation" makes more precise estimates. The least-converged elements or rating-scale categories are shown (largest residual, largest residual percent, largest logit change). We want max.= to approach 0.

Subset connection O.K.

Facets confirms that all elements can be measured unambiguously in one frame of reference.

more JMLE iterations

Iteration 15 Largest Residuals |----------Score------------| logit Measure

Facet Name No./Cat Raw Expected Residual Resd% Value Change

>=============================================================================<

Scale: ?B,?B,?,CREATIVI 4 31 30.8 .2 .6 -1.477 -.001

Scale: ?B,?B,?,CREATIVI 1 4 4.0 .0 -.7 -.644 -.009

Traits Enthusiasm 5 58 58.4 -.4 -.2 .498 .004

Junior Sc Betty 2 79 78.7 .3 .2 .638 .005

Junior Sc Fred 6 39 39.3 -.3 -.2 -.562 -.004

Iteration 15 JMLE max.= -.4 -.2 max.= .005

JMLE ceases when the max.= values are smal, and the convergence criteria are met. If the maximum residual does not decrease noticeably per iteration, then Estimation menu, "Bigger".. If the maximum residual oscillates between large positive and negative values, then Estimation menu "Reduce".

Column headings have the following meanings:

Facet = Name of the facet, as given in specifications or "Scale:" if details apply to a category of a rating scale (or partial credit).

Name = Name of element within Facet or model statement of a rating scale (or partial credit)

No./Cat = Number of element within facet or category number of a rating scale (or partial credit)

Score

Raw = Raw score (= sum of categories, after renumbering if necessary), or count of responses in category, an integer

Expected = Score or count expected based on current estimates, in tenths

Residual = Difference between observed Score and Expected score, in tenths

Resd% = Residual/(Maximum score - minimum score)%.

Logit Measure

Value = Revised estimate of parameter in log-odds units (logits) as a result of this iteration.

Change = Change in logit estimate from logit estimate of the previous iteration.

max.= is the maximum change or residual corresponding to any element, used to determine convergence.

Iteration = The number of times PROX or JMLE has been applied to the data.