Age and modality subset models

An age and modality subset model with two predictors was the best model for predicting tense marker stimulability for copula is and are, -3s, -ed, auxiliary do, and auxiliary was and were.

Age coefficients were positive for all seven of these tense markers. In models where the main effect of age was a significant predictor of tense marker stimulability, the odds of a child being stimulable for that tense marker increased with age when communication modality was held constant. Modality coefficients also were positive for all seven of these tense markers. In models where the main effect of communication modality was a significant predictor of tense marker stimulability, the odds of a child being stimulable for that tense marker were higher in the spoken modality than the graphic symbol modality when age was held constant. Predicted probabilities of stimulability for all six of these tense markers are plotted in Figure 4.6, with 95%

confidence bands.

For copula is stimulability, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 10.92, p < 0.01. The main effect of age was a significant predictor of copula is stimulability, b = 0.16, SE = 0.06, p = 0.01. Increasing age by one month increased the odds of a child being stimulable for copula is by a factor of 1.175 when communication modality was held constant. The main effect of communication modality was not a significant predictor of copula is stimulability even though it was included in the model, b

= 1.59, SE = 0.86, p = 0.06.

For auxiliary do stimulability, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 7.85, p = 0.02. The main effect of communication modality was a significant predictor of auxiliary do stimulability, b = 1.77, SE = 0.82, p = 0.03.

When age was held constant, testing a child in the spoken modality instead of the graphic symbol

Copula is Auxiliary do Auxiliary were Copula are

-ed Auxiliary was -3s

Figure 4.6. Predicted probability of tense marker stimulability in models with age and modality parameters.

modality increased the odds of that child being stimulable for auxiliary do by a factor of 5.875.

Although age was included in the model, the main effect of age was not a significant predictor of auxiliary do stimulability, b = 0.11, SE = 0.06, p = 0.06.

For auxiliary were stimulability, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 10.78, p < 0.01. The main effect of communication modality was a significant predictor of auxiliary were stimulability, b = 3.05, SE

= 1.21, p = 0.01. When age was held constant, testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child being stimulable for auxiliary were by a factor of 21.148. Although age was included in the model, the main effect of age was not a significant predictor of auxiliary were stimulability, b = 0.10, SE = 0.07, p = 0.12.

For copula are stimulability, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 17.41, p < 0.01. The main effects of age, b = 0.20, SE

= 0.07, p < 0.01 and communication modality, b = 2.21, SE = 0.94, p = 0.02 were both significant predictors of copula are stimulability. Increasing age by one month increased the odds of a child being stimulable for copula are by a factor of 1.227 when communication modality was held constant. When age was held constant, testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child being stimulable for copula are by a factor of 9.131.

For -ed stimulability, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 20.36, p < 0.01. The main effects of age, b = 0.18, SE = 0.08, p = 0.02 and communication modality, b = 3.51, SE = 1.16, p < 0.01 were both significant predictors of -ed stimulability. Increasing age by one month increased the odds of a child being stimulable for -ed by a factor of 1.201 when communication modality was held constant. When

age was held constant, testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child being stimulable for -ed by a factor of 33.506.

For auxiliary was, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 13.23, p < 0.01. The main effects of age, b = 0.19, SE = 0.08, p = 0.02 and communication modality, b = 2.80, SE = 1.09, p = 0.01 were both significant predictors of auxiliary was stimulability. Increasing age by one month increased the odds of a child being stimulable for auxiliary was by a factor of 1.206 when communication modality was held constant. When age was held constant, testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child being stimulable for auxiliary was by a factor of 16.453.

For -3s stimulability, the age and modality subset model was significantly better than an intercept model, likelihood ratio = 6.85, p = 0.03. Although both of these predictors were included in the model, neither the main effect of age, b = 0.09. SE = 0.05, p = 0.09 nor the main effect of communication modality, b = 1.18, SE = 0.71, p = 0.10 were significant predictors of -3s stimulability.

4.3.2 Question 2B.

Figure 4.7 shows the predicted proportion of correct probe item responses on stimulability tests for each morpheme category as a function of the significant fixed effects. These plots include 95% confidence bands. Fixed effects for each model are discussed in the following paragraphs.

COPULA BE -3s

-ed AUXILIARY DO

AUXILIARY BE

Figure 4.7. Predicted proportions of correct responses on category stimulability tests.

No significant age-by-modality interaction effects were found for COPULA BE category stimulability, b = -0.04, SE = 0.07, p = 0.58, -3s category stimulability, b = -0.05, SE = 0.10, p = 0.63, -ed category stimulability, b = -0.03, SE = 0.11, p = 0.79, or AUXILIARY DO category stimulability, b = -0.12, SE = 0.10, p = 0.26. This indicates that category stimulability grows at the same rate across communication modalities for each of these morpheme categories. The interactions were removed, and a second model was formed for each of these morpheme categories using fixed effects for the main effects of age and communication modality.

For AUXILIARY BE, morpheme category stimulability was modulated by a significant age-by-modality interaction, b = -0.24, SE = 0.09, p = 0.01. However, no children younger than 42 months on any AUXILIARY BE stimulability probe items. All children younger than 42 months were removed from the analysis. A second model was formed using data from the 23 children who were at least 42 months old (13 in the graphic symbol modality, 10 in the spoken modality). In this second model, the age-by-modality interaction was not significant, b = -0.23, SE = 0.14, p = 0.08, indicating that AUXILIARY BE category stimulability grows at the same rate across communication modalities after the age of 42 months. The interaction was removed, and a third model was formed using fixed effects for the main effects of age and communication modality.

The main effects of age were significant predictors of morpheme category stimulability in main effects models of COPULA BE category stimulability, b = 0.13, SE = 0.03, p < 0.01, -ed category stimulability, b = 0.16, SE = 0.05, p < 0.01, AUXILIARY DO category stimulability, b

= 0.10, SE = 0.05, p = 0.04, and the main effects model of AUXILIARY BE category stimulability in children at least 42 months old, b = 0.16, SE = 0.07, p = 0.02. Age coefficients were positive in these models, indicating that the odds of a child giving a correct response on any

corresponding COPULA BE, -ed, AUXILIARY DO, or AUXILIARY BE stimulability probe item increased with age when communication modality was held constant. Increasing age by one month increased the odds of a child giving a correct response on any given COPULA BE stimulability probe item by a factor of 1.137 when modality was held constant. Increasing age by one month increased the odds of a child giving a correct response on any given -ed stimulability probe item by a factor of 1.169 when modality was held constant. Increasing age by one month increased the odds of a child giving a correct response on any given AUXILIARY DO stimulability probe item by a factor of 1.103 when modality was held constant. For children at least 42 months old, increasing age by one month increased the odds of a child giving a correct response on any given AUXILIARY BE stimulability probe item by a factor of 1.176 when modality was held constant. The main effect of age was not a significant predictor of morpheme category stimulability in the main effects model of -3s category stimulability, b = 0.10, SE = 0.05, p = 0.06.

The main effects of communication modality were significant predictors of morpheme category stimulability in main effects models of -3s category stimulability, b = 2.31, SE = 0.69, p

< 0.01, -ed category stimulability, b = 3.15, SE = 0.64, p < 0.01, and AUXILIARY DO category stimulability, b = 1.60, SE = 0.66, p = 0.02. Testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child giving a correct response on any given -3s stimulability probe item by a factor of 10.107 when age was held constant. Testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child giving a correct response on any given -ed stimulability probe item by a factor of 23.278 when age was held constant. Testing a child in the spoken modality instead of the graphic symbol modality increased the odds of that child giving a correct response on any given AUXILIARY

DO stimulability probe item by a factor of 4.954 when age was held constant. The main effects of communication modality were not significant predictors of morpheme category stimulability in the main effects model of COPULA BE category stimulability, b = 0.72, SE = 0.42, p = 0.08 or the main effects model AUXILIARY BE category stimulability in children at least 42 months old, b = 0.85, SE = 0.52, p = 0.11.

4.3.3 Question 2C.

Predicted probabilities of morpheme category stimulability as a function of age and morpheme category in each modality are shown in Figure 4.8.

Spoken Modality Graphic Symbol Modality

Figure 4.8. Predicted proportions of correct responses on stimulability across morpheme categories in the spoken and graphic symbol modalities.