# Aggregate scores¶

“Aggregate scores” is an automatic scoring system to enable better and more user-friendly functions for LHQ. Four aggregated scores are designed to represent participants’ overall proficiency, dominance, and immersion levels of each language they have learned. These scores will help the researcher to arrive promptly at a useful estimation/ classification of different types of multilingual speakers.

## Aggregate scores calculation¶

Through the Calculation Parameters panel, you can calculate the required aggregate scores by designate the weighting distribution for the four components (Reading, Writing, Listening and Speaking). The rationale is that different researchers may have different needs on which component should be emphasized in their studies, therefore it is more flexible for a researcher to use a weighted aggregated scores in given instances: for example, a study focusing on illiterate bilinguals may only consider speaking and listening, with 50% weighting to each of them (0% for reading and writing).

## Language proficiency¶

The aggregated scoring of proficiency based on the weighted sum of a participant’s self-rating of his proficiency levels on different components of a language (Question 15: Rate your current ability in terms of listening, speaking, reading, and writing in each of the languages you have studied or learned).

A participant’s overall proficiency score of his ith language can be written as:

$Proficiency_{i} = \frac{1}{7}\sum_{j=\{R,L,W,S\}}ω_{j}P_{i,j}$

Here, {R,L,W,S} stands for Reading, Listening, Writing and Speaking components of a language.

Pi,j stands for a participant’self-rated proficiency level to the jth component of his ith language.

Since it is rated on a 7-point Likert scale, we use a scaling factor of 1/7 to normalize it into a range between zero and one (with 1 indicating the native language-like proficiency level).

ωj represents a weight assigned to the jth linguistic component.

## Language immersion¶

The aggregated scoring of immersion for each language that the participant knows, based on her Age, Age of Acquisition (AoA), and Years of Use of the language (Question 7 of LHQ 3.0: Indicate your native language(s) and any other languages you have studied or learned, the age at which you started using each language in terms of listening, speaking, reading, and writing, and the total number of years you have spent using each language).

A participant’s overall immersion score of his ith language can be written as:

$Immersion_{i} = \frac{1}{2}[\sum_{j=\{R,L,W,S\}}ω_{j}(\frac{Age-AOA_{ij}}{Age}+(\frac{YoU_{i}}{Age})]$

Here, Age is the participant’s current age in years.

AOAi,j stands for the participant’s age of starting using her ith language in terms of the jth component (e.g., reading).

YoUi stands for her total number of years using the ith language.

{R,L,W,S} stands for Reading, Listening, Writing and Speaking components of a language.

ωj represents a weight assigned to the jth linguistic component.

In addition, we apply a scaling factor (1/2) to the function to ensure AoA and YoU have equal weight on calculating the overall immersion score, and to normalize the score to a range between 0 and 1 (with 1 indicating the most native-like immersion level into a language).

## Language dominance¶

The aggregated scoring of dominance based on both the participant’s self-reported proficiency (Question 15, see above) and the time (hours per day) spent on different components of each language (Questions 18, Estimate how many hours per day you spend engaged in the following activities in each of the languages you have studied or learned; Question 19. Estimate how many hours per day you spend speaking with the following groups of people in each of the languages you have studied or learned).

A participant’s overall dominance score of his ith language can be written as:

$Dominance_{i} = \sum_{j=\{R,L,W,S\}}ω_{j}[\frac{1}{2}(\frac{P_{ij}}{7})+\frac{1}{2}(\frac{H_{ij}}{K})]$

Here, Pi,j stands for a participant’self-rated proficiency level to the jth component of his ith language.

Hi,j stands for the total estimated hours per day a participant spent on the jth linguistic aspect (e.g., speaking) of her ith language.

K is a constant serving as a scaling factor, currently set to be 16.

Another scaling factor 1/2 is applied to the function to ensure the proficiency and the daily usages of a language to have equal weight on calculating its dominance score.

{R,L,W,S} stands for Reading, Listening, Writing and Speaking components of a language.

ωj represents a weight assigned to the jth linguistic component.

## Ratio of dominance¶

A word of caution regarding the aggregated dominance scores: although useful for within-subject comparison of language dominance, one should be careful about using these scores for comparing across participants. The main reason is that there are large individual differences on participants’ self-estimation of their daily usage of one or more languages. Some participants may be more liberal when estimating their time on language activities, thus giving overall higher dominance scores; whereas others are more conservative when estimating.

To overcome this potential pitfall, we introduce another new measurement of language dominance, expressed as a ratio between two dominance scores, as

$Ratio_{Dominance} = \frac{Dominance_{i}}{Dominance_{1}}$

This measurement provides the relative ratio of the dominance score of each language (Dominancei) against that of the first (typically native, Dominance1) language that a participant reports. It can give researchers a standardized estimate of language dominance that is more comparable across participants (like Z scores). Using the ratio, the researcher can easily determine if a participant is a balanced multilingual, or is someone having one language dominant over another language.

## MLD score¶

The Multilingual Language Diversity (MLD) score allows researcher better describe bilingualism through language usage in terms of context and diversity.

The MLD score is calculated as follows:

For the ith language reported by a participant, LHQ3 calculates an aggregated dominance score (Dominancei) based on both the participant’s self-reported proficiency and frequency of usage time (hours per day) on different components of the language. A temporary variable for the ith language that we term as Proportion of Dominance (PD i):

$PD_{i} = \frac{Dominance_{i}}{\sum_{i=1}^{n}Dominance_{i}}$

where n represents the total possible languages a participant has learned. PDi roughly represents the proportion of a languagei (ith language) that is dominant in a participant’s language environment/usage.

The participant’s overall MLD score is then calculated in a form of Shannon Entropy.

$MLD = -\sum_{i=1}^{n}PD_{i}\log_2(PD_{i})$

MLD will be in a range between 0 and 2.