There was no significant difference in daily tyrosine intake between the age groups, t(1717) = 1.20, p = 0.23. Younger participants consumed an average of 2.85 g of tyrosine daily (SD 1.36, range 1–17 g) and older participants 2.77 g (SD 0.946, range 1–10). Likewise, the average food intake (in g) did not differ between the age groups, t(1722) = − 1.59, p = 0.11, with younger participants consuming 1345 g (SD 413) and older participants consuming 1383 g per day (SD 390). However, we did observe a significant difference in body mass index (younger participants: mean = 23.39, SD 4.26, older participants: mean = 26.82, SD 4.11, t(1712) = − 13.64, p < 0.001). In cognitive performance, strong differences were observed between age groups in all test scores, with younger outperforming older participants (see Table 1).

Table 1 Group differences in cognitive performance between the two age groups Full size table

CFA of cognitive performance indicators across groups

Confirmatory factor analysis (CFA) was conducted to define the three latent factors of individual differences in WM, EM, and Gf across both age groups. The first model was a configural invariance model, with the same pattern of fixed and free factor loadings across groups. This model had a significant Chi-square index, χ2 (48) = 125.75, p < 0.001, but acceptable fit to the data, with CFI = 0.979, TLI = 0.968, RMSEA = 0.043, and BIC = 56184.2.

The next model estimated the weak factorial invariance model with invariant factor loadings across the younger adult and older adult groups. This model also had a significant Chi-square index, χ2 (54) = 155.97, p < 0.001, and the change in statistical fit was statistically significant, ∆χ2 (6) = 30.22, p < 0.001. However, the practical fit indices were altered little, with CFI = 0.972, TLI = 0.962, and RMSEA = 0.047, and the BIC = 56169.7 was lower, indicating that this model had better fit to the data than did the configural model.

The third model was the strong factorial invariance model, which imposed cross-group invariance constraints on measurement intercepts. The strong factorial invariance model fit decidedly worse than the weak invariance model, χ2 (60) = 224.47, p < 0.001, and the change in statistical fit was significant, and the change in fit was large, ∆χ2 (6) = 68.50, p < 0.001. Moreover, the practical fit indices were noticeably worse, with CFI = 0.955, TLI = 0.945, and RMSEA = 0.056, and the BIC = 56193.5 increased, demonstrating poor fit of this model. Based on modification indices, we relaxed one intercept invariance constraint on the Letter Updating variable resulting in a partial strong invariance model, which exhibited considerably improved fit, with χ2 (59) = 169.09, p < 0.001, and a large improvement in fit over the full strong invariance model, ∆χ2 (1) = 55.38, p < 0.001. The practical fit indices were much improved, with CFI = 0.970, TLI = 0.963, and RMSEA = 0.046, and the BIC = 56145.6 was the lowest of all models considered to this point, suggesting that the partial strong invariance model is tenable and is the optimal model for these data.

Parameter estimates for the partial strong factorial invariance model are shown in Table 2, which provides the raw score estimates of all parameters. As shown in Table 2, the model was identified by fixing factor means to 0.0 and factor variances to 1.0 in the younger adult group, estimating factor correlations for the younger adult group, constraining factor loadings and intercepts to invariance across groups, and estimating factor means, variances, and covariances in the older adult group. All parameter estimates were significant at p < 0.0001. Standardized factor loadings were in the moderate-to-strong range, with median standardized loadings of 0.65 in each group. As shown in Table 2, the WM and Gf factors were highly correlated in both samples, and correlations of the EM factor with the WM and Gf factors were weaker, but still large in magnitude, as predicted.

Table 2 Multiple-group confirmatory factor analysis for nine cognitive performance variables for young and older adults Full size table

The most important pattern in the results was the large mean differences on latent factors across groups. Because the model was identified with latent variables means of 0 and SDs of 1.0 in the younger adult sample, the mean differences on latent factors for the older group were in a Cohen’s d metric. The mean differences in performance showed that the older adult group scored more than 2 SD units below the younger adult group on all three factors, with mean differences of − 2.43 (SE = 0.16) on the WM factor, − 2.65 (SE = 0.22) on the EM factor, and − 2.18 (SE = 0.15) on the Gf factor. Thus, the mean differences in performance across groups were substantial.

Associations with tyrosine

We hypothesized that individuals’ tyrosine intake would be linked to their current cognitive status. In this model, our primary predictor of performance on the cognitive factors (WM, EM, and Gf) was tyrosine intake, and sex, education, age, and average food intake were control variables. The effects of tyrosine intake, sex, education, age, and average food intake on the cognitive factors were allowed to vary across the young adult and old adult groups, so we termed this model an initial unconstrained model. The fit of this model, which retained the partial strong invariance measurement constraints on cognitive factors, was acceptable. The Chi-square index was significant, χ2 (124) = 262.35, p < 0.001, but the model exhibited close fit to the data, with CFI = 0.976, TLI = 0.965, RMSEA = 0.036, and BIC = 80493.9.

We then constrained the path coefficients from tyrosine to the cognitive factors and average food intake to the cognitive factors to invariance across the younger adult and older adult groups to test whether effects of tyrosine and food intake on cognition differed across groups. The cross-group invariance constraints on effects of tyrosine and food intake on Gf led to a non-significant change in model fit, ∆χ2 (2) = 3.59, p = 0.17. Invariance constraints on effects of tyrosine and food intake on WM were also non-significant, ∆χ2 (2) = 0.50, p = 0.64. Invariance constraints on effects of tyrosine and food intake on EM were also non-significant, ∆χ2 (2) = 0.89, p = 0.91. Finally, the omnibus constrained model invoked cross-group invariance constraints of tyrosine and food intake simultaneously on all three cognitive factors. This model had a significant statistical index of fit, with χ2 (130) = 271.54, p < 0.001, but the change in fit from the initial unconstrained model was small and non-significant, ∆χ2 (6) = 9.19, p = 0.30. Moreover, the practical fit indices were either unchanged or improved, with CFI = 0.975, TLI = 0.966, and RMSEA = 0.035. Finally, the BIC = 80458.4 was lower (i.e., improved), indicating that the cross-group invariance constraints on parameter estimates did not harm model fit. We thus accepted this model as the final model for the data.

Standardized parameter estimates from our final model are shown in Fig. 1. Inspection of Fig. 1 reveals that factor loadings in the young adult sample were in the moderate-to-strong range (median loading = 0.66) and were of similar magnitude in the older adult sample (median loading = 0.64). We found significant direct effects of tyrosine on Gf in the young adult sample, β = 0.26 (SE = 0.07), p < 0.001, and in the older adult sample, β = 0.13 (SE = 0.04), p < 0.001. Tyrosine also had significant effects on WM in the young adult sample, β = 0.23 (SE = 0.07), p < 0.001, and in the older adult sample, β = 0.12 (SE = 0.04), p < 0.001. The effects of tyrosine on EM were also significant, in the young adult sample, β = 0.17 (SE = 0.07), p = 0.02, and in the older adult sample, β = 0.11 (SE = 0.05), p = 0.02. Effects of predictors explained 6% of the variance of Gf, 6% of the variance of WM, and 13% of the variance of EM in the young adult sample, and 21% of the variance in Gf, 14% of the variance in WM, and 21% of the variance of EM in the older adult sample.

In Table 3, within-group standardized regression coefficients are reported, along with the variance explained for each ability factor in each sample. The greater variance explained in the older adult group relative to the young adult group on the three ability factors of Gf, WM, and EM is due primarily to the effects of covariates, in particular the effect of education. In the young adult group, the direct effect of education explained between 2% (0.15 squared = 0.023, for EM) and 3% (0.18 squared = 0.032, for Gf) of the variance of the three ability factors. In contrast, the direct effect of education explained between 9.6% (0.31 squared = 0.096, for WM) and 15% (0.39 squared = 0.152, for Gf) of the variance of the three ability factors. The positive signs of the regression weights for education reflect the tendency for persons with higher levels of education to have higher scores on ability dimensions. In addition, the much stronger coefficients for education in the older adult sample are consistent with prior research investigating education as a proxy for cognitive reserve, which counteracts the negative effects of aging of human abilities. Inspection of Table 3 will also show that the effect of age on ability factors was very weak in the young adult sample, but relatively much stronger in the older adult sample, with the negative sign of these age coefficients consistent with widely reported aging declines on ability dimensions in old age. Thus, the higher levels of explained variance in the older adult sample is primarily due to the much stronger effects of education and moderately stronger effects of age on the ability factors in the older adult sample relative to the young adult sample.

Table 3 Standardized regression weights when regressing ability factors on covariates, food intake, and tyrosine: by sample Full size table

Exploring the categories of dietary intake providing tyrosine

In general, tyrosine intake was most strongly associated with participants’ amount of reported meat product intake (young: r (338) = 0.868, p < 0.001, old: r (1375) = 0.851, p < 0.001). All other correlation coefficients were of clearly smaller magnitude and below r = 0.30.