A mixed latent class Markov approach for estimating labour market mobility with multiple indicators and retrospective interrogation
Section 4. Results: Comparisons of mixed and standard LCM models

We estimate various specifications of the standard and mixed LCM models. The standard model consists of two parts: structural, describing true dynamics among latent variables (true states) by a first-order Markov chain; and measurement, which links each latent variable to its indicators (observed conditions in the labour market). Some restrictions incorporating a priori information and/or assumptions are imposed on the parameters of the measurement part, based on evidence from observed data (inconsistencies and transitions) and on findings from the survey methodology and cognitive psychology literature on the error - generating mechanism. Only four of the nine rotation groups supplying information referring to one calendar year were interviewed in every quarter, and only for two of these groups do we have all three indicators of labour market conditions (see Table 3.1). For the other two groups, we do not have the information collected with the retrospective question. The pattern of missing information due to the rotation design of the survey is included in the estimated LCM models as data missing at random.

All estimated models share the following characteristics: true transitions follow a first-order Markov chain; (Due to the survey design, there were no individuals observed for three consecutive waves, i.e., a second-order Markov chain cannot be estimated, since the relative sufficient statistics are missing. However, although the labour market condition in one quarter may very plausibly affect the condition in the subsequent quarter, that it may do so in a significant manner after two quarters is far less plausible.) classification errors are assumed constant over time for each indicator; the ICE assumption is included. Model fit is evaluated by the BIC (Bayesian information criterion) index because of the large sample size (average 250,000 units per year; see Table 4.1)

The specification of a mixed LCM model is also recommended by the fact that the sample may contain various groups of respondents with different behaviour in the labour market. As already noted, the recent literature shows that not taking unobserved heterogeneity in transitions into account when estimating LCM models may result in biased estimates of measurement error (Magidson et al. 2007). In addition, a mixed LCM model may give the data a better fit.

We estimate a mover-stayer LCM model with the assumption of constant measurement errors across the two latent groups. It should be noted that all estimated models were identified and that, in order to reduce the risk of detecting local maxima, estimation was performed several times with different sets of starting values. Latent Gold 4.5 software was implemented (Vermunt and Magidson 2008).

Table 4.1 compares the mixed and standard LCM models fitted to our five data samples, referring to the years from 2005 and 2009 and using the BIC index. The mixed model shows a better fit for all samples. Table 4.2 lists the percentages of movers and stayers in the first quarter of 2005, and the distribution of the two unobserved groups in the first quarter of each year. Clearly, unobserved heterogeneity is highly correlated with the initial state and, as expected, stayers are either employed or not in the labour market, i.e., only a very small percentage is unemployed.

Table 4.1
Comparison of standard and mixed LCM models: BIC index
Table summary
This table displays the results of Comparison of standard and mixed LCM models: BIC index. The information is grouped by Year (appearing as row headers), n, Standard and Mixture (appearing as column headers).
Year n Standard Mixture
2005 220,051 650,241 649,401
2006 206,037 587,794 587,058
2007 274,484 748,788 748,654
2008 277,363 667,399 666,335
2009 274,723 747,997 746,991
Table 4.2
Mixed LCM model: proportion of movers and stayers and distribution in initial state 2005, I quarter, %
Table summary
This table displays the results of Mixed LCM model: proportion of movers and stayers and distribution in initial state 2005 Proportion, E, U and N (appearing as column headers).
Proportion E U N
Movers 10.23 39.85 39.09 21.06
Stayers 81.79 41.79 3.36 54.85

As the data in Tables 4.3-4.5 show, (Labour market composition, estimated transitions and estimated measurement errors show the same pattern in the other three quarters of each year.) the better fit to the data of the mixed model is all due to the different estimated transition rates; labour market composition and estimated measurement errors are the same in both models. This result is the opposite of that obtained by Magidson et al. (2007), who compared the mover-stayer and standard LCM models applied to labour market transitions from the Current Population Survey. The above authors found that the mixed LCM model provides a better fit to the data than the standard LCM model and that the latter, not taking unobserved heterogeneity into account, overestimates the degree of measurement error with respect to the mover-stayer model. In detail, the above authors used simulated results to estimate a violation of homogeneous transition probabilities, so that heterogeneity correlated with the initial state produces inflated estimates of measurement errors in a standard LCM model.

Table 4.3
Comparison of standard and mixed LCM models: labour market composition I quarter 2005, %
Table summary
This table displays the results of Comparison of standard and mixed LCM models: labour market composition I quarter 2005 E, U and N (appearing as column headers).
E U N
2005 Standard 41.67 7.00 51.33
Mixture 41.59 7.02 51.39
Table 4.4
Comparison of standard and mixed LCM models: estimated transitions I quarter to II quarter 2005 – 2009, %
Table summary
This table displays the results of Comparison of standard and mixed LCM models: estimated transitions I quarter to II quarter 2005 – 2009 EE, EU, EN, UE, UU, UN, NE, NU and NN (appearing as column headers).
EE EU EN UE UU UN NE NU NN
2005 Standard 97.36 1.32 1.32 15.59 76.18 8.23 0.57 0.74 98.69
Mixture 96.46 1.68 1.86 19.61 69.65 10.74 0.91 1.09 98.00
2006 Standard 96.75 1.68 1.56 19.52 71.27 9.21 1.01 0.99 90.00
Mixture 96.22 1.92 1.87 22.11 66.96 10.93 1.25 1.22 97.54
2007 Standard 96.69 1.67 1.64 18.84 70.56 10.60 1.01 0.99 98.00
Mixture 96.42 1.80 1.78 20.22 67.80 11.98 1.10 1.45 95.45
2008 Standard 97.56 1.41 1.03 15.86 79.73 4.42 0.53 0.62 98.85
Mixture 96.45 1.89 1.66 19.56 73.25 7.19 0.83 0.89 98.28
2009 Standard 96.85 1.71 1.44 14.04 75.33 9.63 1.04 1.01 97.95
Mixture 96.27 1.95 1.78 17.09 71.16 11.75 1.30 1.22 97.48
Table 4.5
Comparison of Standard and mixed LCM models: estimated measurement errors I quarter 2005 – 2009, %, ILO indicator
Table summary
This table displays the results of Comparison of Standard and mixed LCM models: estimated measurement errors I quarter 2005 – 2009 EE, EU, EN, UE, UU, UN, NE, NU and NN (appearing as column headers).
EE EU EN UE UU UN NE NU NN
2005 Standard 99.82 0.01 0.17 6.17 45.04 48.80 0.89 0.50 98.61
Mixture 99.82 0.01 0.17 6.16 45.06 48.78 0.90 0.51 98.59
2006 Standard 99.83 0.01 0.16 6.50 41.92 51.58 0.75 0.45 98.80
Mixture 99.87 0.01 0.13 5.17 37.28 57.55 0.68 0.40 98.92
2007 Standard 99.75 0.01 0.24 6.84 39.83 53.34 0.75 0.47 98.79
Mixture 99.75 0.01 0.24 6.77 39.92 53.31 0.77 0.47 98.76
2008 Standard 99.83 0.01 0.17 3.81 42.45 53.74 0.61 0.38 99.02
Mixture 99.83 0.01 0.17 3.82 42.41 53.76 0.62 0.38 99.00
2009 Standard 95.34 0.98 3.68 18.30 41.17 40.53 2.06 1.61 96.33
Mixture 95.22 2.34 2.44 15.60 68.02 16.37 1.74 2.14 96.13

The mover-stayer model describes a more dynamic labour market, especially for unemployed respondents: the probability of remaining unemployed over the quarter is lower than that estimated by the standard model.


Report a problem on this page

Is something not working? Is there information outdated? Can't find what you're looking for?

Please contact us and let us know how we can help you.

Privacy notice

Date modified: