Within-Individual Age-Related Trends, Cycles, and Event-Driven Changes in Job Performance: a Career-Span Perspective

Abstract

Past research on age-related differences in job performance have focused primarily between-person comparisons. In the present study, we examine within-individual changes in supervisor-rated job performance to examine the influence of age-related trends, cycles, and event-driven factors. Our analysis is based on an eight-wave dataset from a multiple-cohort sample of employees (N = 750) varying in age from 25 to 65 years. We used an age-sequential design to disentangle maturation effects from historical effects. Results showed that population-level, within-individual change in a general measure of job performance was characterized by an increase in the first phase of the career (workers of 25–30 years), and then by a progressive decline. Within-individual levels of job performance were generally higher for younger workers than for older workers, and mostly reflected the influence of population-level trends but some even-driven effects as well. Results were in line with predictions from Baltes and Baltes’s (1990) meta-theory of selective optimization with compensation and the effects of age-related losses on performance. Results also provide insights into understanding the job performance trajectory over the career span.

Appendix 1. Variance Decomposition

As explained in the main text, the LC-LSTM allows the evaluation of mean-level changes in job performance. Formally, the model presented in our paper can be formulated as follows:

$$ {\eta}_t^{(k)}={\xi}_1^{(k)}+{\gamma}_{2t}^{(k)}{\xi}_2^{(k)}+{\zeta}_t^{(k)}, $$

(1)

where ${\eta}_t^{(k)}$is the latent attribute (in this case job performance) at each time;${\xi}_1^{(k)}+{\gamma}_{2t}^{(k)}{\xi}_2^{(k)}$represents the latent trajectory of the attribute over time; and ${\zeta}_t^{(k)}$represents temporal effects that reflect the impact of time-specific influences, after the removal of both the measurement error, ${\varepsilon}_{jt}^{(k)},$and the variable-specific components, ${\nu}_{jt}^{(k)}$. Time or measurement periods, age groups, and items are indexed by t, k, and j, respectively. Finally, the latent trajectory is represented by two basis curves, ${\gamma}_{1t}^{(k)}\equiv 1$and ${\gamma}_{2t}^{(k)}$. Lastly, only 33 elements of the gamma matrix are estimated (the pattern is given in the next paragraph); note that the second basis curve will vary over time. More concretely, for our data (5 items at 8 time points), the model (in matrix notation) becomes:

$$ {\boldsymbol{y}}^{\left(\boldsymbol{k}\right)}=\boldsymbol{\tau} +\varLambda \left[{\varGamma}^{(k)}{\boldsymbol{\xi}}^{\left(\boldsymbol{k}\right)}+\kern0.5em {\boldsymbol{\zeta}}^{\left(\boldsymbol{k}\right)}\right]+{\boldsymbol{\varepsilon}}^{\left(\boldsymbol{k}\right)}, $$

(2)

with age groups indexed by k = 1, 2 ..., 6, where τ represents the intercepts of the items, Λ represents the factor loadings for the first-order factors (i.e. job performance), at the first-order, this model maintains stationarity and invariance on items’ intercepts and factor loadings across time and age groups, respectively. ε^(k)represents the unique (specific and error) factors. For the second-order factors, Γ^(k)contains the basis curves for the second-order factors representing the intercept and the “slope” (${\gamma}_{2t}^{(k)}$), and ζ^(k)represents the temporal effects. Finally, ξ^(k) includes the individual difference variables for the intercept and “slope.” The observed means for each item at each time had a mean structure:

$$ {\mu}_{Y_{jt}}^{(k)}={\tau}_j+{\lambda}_j\left[{\kappa}_1^{(k)}+{\gamma}_{2t}^{(k)}{\kappa}_2^{(k)}\right], $$

(3)

where ${\kappa}_1^{(k)}\equiv {\hat{\mu}}_{\xi_1}^{(k)}$and ${\kappa}_2^{(k)}\equiv {\hat{\mu}}_{\xi_2}^{(k)}$represents the mean of the intercept and “slope” for the latent curve, respectively.

Given the previously developed LC-LSTM, variance decomposition of the total variance to permanence (latent curve) + temporal + item-method + variable-specific + random error variances can be carried out by assuming that the specific factor has the same covariance across time. Specifically, the covariance between the jth item-specific factor is the same across time (i.e., ${\sigma}_{\nu_{jt}{\nu}_{j{t}^{\prime }}}$is equal for all pairs of time). Under these assumptions and definitions, we can relate the measured variable variances, ${\sigma}_{Y_{jt}}^{(k)2}$, ${\sigma}_{Y_{jt}}^2$and covariances, ${\sigma}_{Y_{jt}{Y}_{j^{\prime }t}\prime}^{(k)}$, to the variances and covariances, ${\sigma}_{\xi_l{\xi}_l\prime }$, of the latent constructs; the temporal variances,${\sigma}_{\zeta_t}^{(k)2}$; ${\sigma}_{Y_{jt}}^2{\sigma}_{\zeta_t}^2$the item-method covariance, ${\sigma}_{\varepsilon_{1t}{\varepsilon}_{4t}}^{(k)}$; the variance-specific variances, ${\sigma}_{\nu_j}^{(k)2};$${\sigma}_{{\nu_j}^{,}}^2$and random error variances,${\sigma}_{\varepsilon_{jt}}^{(k)2};$ and to the item slopes, λ_j, and the elements of the basis curves, ${\gamma}_{lt}^{(k)}$. These relationships are used in the sequential estimation and variance decomposition procedures. The variance of the observed variable,${Y}_{jt}^{(k)},$ is given by

$$ {\sigma}_{Y_{jt}}^{(k)^2}={\lambda}_j^2{\sum}_{l=1}^{l=2}{\sum}_{l^{\prime }=1}^{l^{\prime }=2}{\gamma}_{lt}^{(k)}{\gamma}_{l^{\prime }t}^{(k)}\ {\sigma}_{\xi_l{\xi}_{l\prime }}+{\lambda}_j^2{\sigma}_{\zeta_t}^{(k)2}+{\sigma}_{\nu_j}^{(k)2}+{\sigma}_{\varepsilon_{jt}}^{(k)2}. $$

(4)

The covariance of two different observed variables (j ≠ j') at the same time is:

$$ {\sigma}_{Y_{jt}{Y}_{j^{\prime }t}}^{(k)}={\lambda}_j{\lambda}_{j^{\prime }}{\sum}_{l=1}^{l=2}{\sum}_{l^{\prime }=1}^{l^{\prime }=2}{\gamma}_{lt}^{(k)}{\gamma}_{l^{\prime }t}^{(k)}\ {\sigma}_{\xi_l{\xi}_{l\prime }}+{\sigma}_{\varepsilon_{jt}{\varepsilon}_{j\prime t}}^{(k)}, $$

(5)

where, in the current situation, the item-method covariance, ${\sigma}_{\varepsilon_{jt}{\varepsilon}_{j\prime t}}^{(k)}\ne 0$, only when j = 1 and j′ = 4.

The covariance of the same observed variable measured at different times (t ≠ t') is:

$$ {\sigma}_{Y_{jt}{Y}_{j{t}^{\prime}}}^{(k)}={\lambda}_j^2{\sum}_{l=1}^{l=2}{\sum}_{l^{\prime }=1}^{l^{\prime }=2}{\gamma}_{lt}^{(k)}{\gamma}_{l^{\prime }{t}^{\prime}}^{(k)}\ {\sigma}_{\xi_l{\xi}_{l\prime }}+{\sigma}_{\nu_j}^{(k)2}. $$

(6)

Finally, the covariance of different observed variables (j ≠ j') measured at different times (t ≠ t') is:

$$ {\sigma}_{Y_{jt}{Y}_{j^{\prime }{t}^{\prime}}}^{(k)}={\lambda}_j{\lambda}_{j^{\prime }}{\sum}_{l=1}^{l=2}{\sum}_{l^{\prime }=1}^{l^{\prime }=2}{\gamma}_{lt}^{(k)}{\gamma}_{l^{\prime }{t}^{\prime}}^{(k)}\ {\sigma}_{\xi_l{\xi}_{l\prime }}. $$

(7)

In sum, the LST model presented in Eq. 4 decomposes the variance of an observed variable, ${Y}_{jt}^{(k)}$Y_jt, into four variance components representing the effects of latent trajectories (i.e., ${\lambda}_j^2{\sum}_{l=1}^{l=2}{\sum}_{l^{\prime }=1}^{l^{\prime }=2}{\gamma}_{lt}^{(k)}{\gamma}_{l^{\prime }t}^{(k)}\ {\sigma}_{\xi_l{\xi}_{l\prime }}\Big)$, time (i.e.,${\lambda}_j^2{\sigma}_{\zeta_t}^{(k)2}$${\lambda}_j^2{\sigma}_{\zeta_t}^2$), variable-specific (i.e.,${\sigma}_{\nu_j}^{(k)2}$${\sigma}_{vj}^2$), and random error (i.e., ${\sigma}_{\varepsilon_{jt}}^{(k)2}$${\sigma}_{\varepsilon_{jt}}^2$).

For each of the 6 age groups, these components may be summed across both time, t = 1,…, T = 8, (or wave) and observed variables, j = 1,.., p = 5, to obtain the instrument variance components:

• a. Permanent (i.e., ${\left({\sum}_{j=1}^{j=p}{\lambda}_j\right)}^2\sum \limits_{l=1}^{l=2}{\sum}_{l^{\prime }=1}^{l^{\prime }=2}\ \left[{\sum}_{t=1}^{t=T}{\gamma}_{lt}^{(k)}{\sum}_{t=1}^{t=T}{\gamma}_{l^{\prime }t}^{(k)}\right]\kern0.5em {\sigma}_{\xi_l{\xi}_{l^{\prime }}}$, or the enduring variance of the construct across time (i.e., the “trait” factor) due to the effect of the latent trajectories;

• b. Ephemeral (i.e., ${\left({\sum}_{j=1}^{j=p}{\lambda}_j\right)}^2\ {\sum}_{t=1}^{t=T}{\sigma}_{\zeta_t}^{(k)2}\Big)$, or variance due to transitory “state” factors;

• c. Item-Method (i.e., 2 ${\sum}_{t=1}^{t=T}{\sigma}_{\varepsilon_{1t}{\varepsilon}_{4t}}^{(k)}$) or variance shared uniquely between items 1and 4;

• d. Item-Specific (i.e., T² ${\sum}_{j=1}^{j=p}{\sigma}_{\nu_j}^{(k)2}$${\sum}_{j=1}^p{\sum}_{t=1}^m{\sigma}_{v_j}^2$), or variance unique to the items and not to the construct;

• e. Random error (i.e., $\sum \limits_{t=1}^{t=T}\sum \limits_{j=1}^{j=p}{\upsigma}_{\varepsilon_{jt}}^{(k)2}$${\sum}_{j=1}^p{\sum}_{t=1}^m{\upsigma}_{\varepsilon_{jt}}^2$), or variance attributed to random error.

Results from variance decomposition are presented in full detail in Tables 3 and 4. Also, they were discussed in the paper. We note that from the above models, systematic, static, and dynamic reliability coefficients can be derived (Tisak & Tisak, 2000). Parenthetically, although these indices can be formulated at an aggregated level, for simplicity these indices are presented at the item level. The index was computed here, in order to offer full detail about the longitudinal behavior of our measure of job performance. The systematic reliability index is the most common and conservative index because it excludes only random error,${\sigma}_{\varepsilon_{jt}}^{(k)2}$) and is computed as follows: 1 − $\frac{\ {\sigma}_{\varepsilon_{jt}}^2}{\sigma_{y_{jt}}^2}$. Static reliability is more stringent, because it also excludes the variable-specific variance component, ${\sigma}_{\nu_j}^2$, from the true score variance, and is computed as follows: 1 − $\frac{\sigma_{\nu_j}^{(k)2}+{\sigma}_{\varepsilon_{jt}}^{(k)2}}{\sigma_{Y_{jt}}^{(k)2}}$. Finally, the dynamic reliability index assesses the ability of the composite to reflect the permanent nature of the attribute, and also excludes the temporal variance, ${\lambda}_j^2{\sigma}_{\zeta_t}^{(k)2}$. It is computed as follows: 1 − $\frac{\lambda_j^2\ {\sigma}_{\zeta_t}^{(k)2}+{\sigma}_{\nu_j}^{(k)2}+{\sigma}_{\varepsilon_{jt}}^{(k)2}}{\sigma_{Y_{jt}}^{(k)2}}$, with the terms defined as above. One can observe that the systematic coefficient will always be higher than the static coefficient, which in turn will always be higher than the dynamic coefficient. Because the estimated proportion of variable-specific variance is small, the systematic and static reliability coefficients are relatively similar and are very high (both > .90). However, given that the ephemeral or temporal effect is large, the dynamic reliability coefficient is noticeably lower than either of the other reliability estimates. In particular, with scale reliability estimates ranging from .34 to .97, these results suggest that if one does not use structural equation modeling, temporal, specific, and random error variances may sometimes contaminate the scale score badly. In conclusion, the present variance decomposition approach clearly reveals important results that could easily have been overlooked if other statistical procedures had been used.

Table 3 Proportions of variance and scale reliability estimates for the job performance measure

Table 4 Proportions of variance and scale reliability estimates for the job performance measure