Doppler-free frequency modulation spectroscopy of atomic erbium in a hollow cathode discharge cell

The erbium atomic system is a promising candidate for an atomic Bose-Einstein condensate of atoms with a non-vanishing orbital angular momentum ($L \neq 0$) of the electronic ground state. In this paper we report on the frequency stabilization of a blue external cavity diode laser system on the 400.91 $nm$ laser cooling transition of atomic erbium. Doppler-free saturation spectroscopy is applied within a hollow cathode discharge tube to the corresponding electronic transition of several of the erbium isotopes. Using the technique of frequency modulation spectroscopy, a zero-crossing error signal is produced to lock the diode laser frequency on the atomic erbium resonance. The latter is taken as a reference laser to which a second main laser system, used for laser cooling of atomic erbium, is frequency stabilized

A hierarchical latent response model for inferences about examinee engagement in terms of guessing and item‐level non‐response

In low‐stakes assessments, test performance has few or no consequences for examinees themselves, so that examinees may not be fully engaged when answering the items. Instead of engaging in solution behaviour, disengaged examinees might randomly guess or generate no response at all. When ignored, examinee disengagement poses a severe threat to the validity of results obtained from low‐stakes assessments. Statistical modelling approaches in educational measurement have been proposed that account for non‐response or for guessing, but do not consider both types of disengaged behaviour simultaneously. We bring together research on modelling examinee engagement and research on missing values and present a hierarchical latent response model for identifying and modelling the processes associated with examinee disengagement jointly with the processes associated with engaged responses. To that end, we employ a mixture model that identifies disengagement at the item‐by‐examinee level by assuming different data‐generating processes underlying item responses and omissions, respectively, as well as response times associated with engaged and disengaged behaviour. By modelling examinee engagement with a latent response framework, the model allows assessing how examinee engagement relates to ability and speed as well as to identify items that are likely to evoke disengaged test‐taking behaviour. An illustration of the model by means of an application to real data is presented

Exploring latent states of problem‐solving competence using hidden Markov model on process data

The response process of problem-solving items contains rich information about respondents' behaviours and cognitive process in the digital tasks, while the information extraction is a big challenge. The aim of the study is to use a data-driven approach to explore the latent states and state transitions underlying problem-solving process to reflect test-takers' behavioural patterns, and to investigate how these states and state transitions could be associated with test-takers' performance. We employed the Hidden Markov Modelling approach to identify test takers' hidden states during the problem-solving process and compared the frequency of states and/or state transitions between different performance groups. We conducted comparable studies in two problem-solving items with a focus on the US sample that was collected in PIAAC 2012, and examined the correlation between those frequencies from two items. Latent states and transitions between them underlying the problem-solving process were identified and found significantly different by performance groups. The groups with correct responses in both items were found more engaged in tasks and more often to use efficient tools to solve problems, while the group with incorrect responses was found more likely to use shorter action sequences and exhibit hesitative behaviours. Consistent behavioural patterns were identified across items. This study demonstrates the value of data-driven based HMM approach to better understand respondents' behavioural patterns and cognitive transmissions underneath the observable action sequences in complex problem-solving tasks