\section{Introduction}

Macro-dynamics such as weather situations, seasons, and regional
opportunity structures have received only little attention in research
on survey methods in general and in research on the survey
participation of panellists in web-based online surveys in particular
\parencite{Potoski2015, Goritz2014, Couper1996}. However,
\textcite{Groves1992} for example stress that, aside from
characteristics of the sampled target persons and attributes of the
survey design, societal-level factors also affect the response
behaviour of invited target persons in web-based surveys. In this
vein, \textcite[185]{Keusch2015} concludes that, while only a few
studies have empirically analysed the impacts of societal-level
factors (such as the accepted legitimacy of sponsors and organizations
conducting scientific surveys, the degree of social cohesion and
integration, or the survey climate and survey fatigue due to the
over-surveying of populations) on survey participation in general,
corresponding knowledge about web-based online surveys is especially
scarce \parencite{Groves1992}. Furthermore, explanations of individual
survey participation emphasize that regional opportunity structures
and their characteristics affect participation and response rates as
well. According to \textcite{Groves1998}, large urban
areas---inner-city areas in large metropolitan areas---generate lower
response rates in social-scientific surveys than rural areas
\parencite[174]{Couper1996}. This may indicate that, compared to rural
areas, urban areas provide more attractive opportunities that
potentially divert target persons from taking part in
social-scientific surveys. In addition, internet access---an essential
precondition for participation in an online survey---differs between
regions, with an obvious urban-rural divide
\parencites[136]{Fan2010}{Couper2000}. Internet access is also
unequally distributed among quartiers, correlating with the living
standard of a quartier's residents. Finally, social integration and
individual isolation related to regional opportunity structures are
considered important for the explanation of response rates, i.e. the
ratio of responding target persons out of the eligible target sample
\parencite{Esser1986}. According to the Social Isolation Hypothesis
\parencites{Groves1998}[see also:][60]{Sassenroth2013}, this means
that socially less integrated and isolated individuals living mostly
in urban areas and feeling disadvantaged by society often tend to
decline cooperation in surveys since they do not share either the
social norm that survey participation is a civic duty, an interest in
social exchange with interviewers, or an appreciation of this type of
social-scientific research.

In addition to such macro-conditions, the paper at hand also
investigates the timing of survey participation by considering
time-varying circumstances at the macro level of a survey. Moving on
to seasons (the macro level), \textcite[158,165]{Goritz2014} confirms
the hypothesis that the starting rate---i.e. the proportion of invited
panellists entering the first page of an online survey---is highest in
winter months, while it is assumed that the retention (i.e. the
completion rate among respondents who have started) is unaffected by
the season in which the survey is carried out.  However, it is found
that the completion rate is higher in seasons other than winter
\parencite[166]{Goritz2014}. The seasonal differences in starting
rates rest on the device and its use: since participating in web-based
online surveys is primarily an indoor activity, it is assumed that
this action is more likely to be performed in winter, while outdoor
activities are more attractive in other seasons. During summer months,
for example, ``a higher share of panellists is on vacation and
therefore less inclined or available to respond to a study request''
\parencite[158]{Goritz2014}. In another experiment,
\textcite{Potoski2015} found that surveys are at risk of
temperature-induced participation. According to their findings,
unusual temperatures seem decisive regarding who takes part in
surveys: wealthier respondents are over-represented in especially cold
and especially warm conditions.

However, it is still an open question whether this finding will be
confirmed when, besides an individual's characteristics, the
above-mentioned opportunity structures as well as the different and
changing weather situations in different seasons and at different
stages of the field period are taken into account. Due to logistical
reasons, it is impossible to conduct all scientific surveys in winter,
which would be the only adequate thing to do according to
\textcite{Goritz2014} finding. Therefore, it is important to know
whether---regardless of the season---``fine'' weather situations are
more likely to divert panellists from responding to a survey
invitation than ``bad'' weather. Presumably, heavy rainfall and cold air
temperatures enforce indoor activities and thereby lead to higher
participation rates than the ones observed during periods of high
temperatures and long hours of sunshine. The latter conditions are
more likely to result in invitees postponing their survey
participation and in their decreasing tendency to respond as time goes
by. Even if they are intuitively plausible, such claims about the
inclination of sampled target persons and the timing of survey
participation have to be tested empirically.

Therefore, this contribution empirically analyses the following
question: how do weather situations affect panellists' inclination to
participate in a scientific online survey when controlling the
seasons, stage of the field period, regional opportunity structure,
and individuals' resources and abilities? This question about the
eligible panellists' inclination and the timing of survey
participation is answered in the context of a multi-wave panel
study. Spell data on panellists' latency is used and event history
analysis, which is suitable for combining micro- and macro-data in a
longitudinal design, is applied.

\section{Theoretical background, previous research, and hypotheses}

For explaining the effect of the weather situation on the inclination
of target persons to take part in an online survey, two theoretical
approaches that have proved to be successful are considered
\parencites[136]{Fan2010}{Goyder2008}. The first theoretical approach
comprises several broad versions of rational action theories, such as
the social exchange theory \parencite{Dillman2000, Dillman2014,
  Hox1996}, the leverage-salience theory \parencite{Groves1998,
  Groves2000}, or the theory of subjective utility
\parencite{Becker2019, Esser1990, Esser1986}. These versions all
assume that an invited individual weighs the consequences of one
action, such as requested survey participation, against the
consequences of alternative activities belonging to the individual's
perceived action set.  Thereby, individuals calculate and evaluate
such consequences based on the costs and benefits of the considered
activities, as well as on the probability of success to receive the
preferred benefits in an optimal way \parencite{Singer2011}. Given
that the subjective expected benefits and costs of different actions
are in a balance so that the individual is indifferent about the
survey participation, few changes in the rather diffuse benefits and
costs could determine the decision between immediate survey
participation, postponement of response, or refusal. In this case, for
example, a prepaid monetary incentive could increase an individual's
inclination to take part in the online survey, since subjective
perceived benefits exceed the costs \parencite{Laurie2009}.

In another case, namely under ``pleasant'' weather conditions, the
opportunity costs of survey participation---i.e. the benefits of
activities forgone as a result of participation---increase due to the
benefits of attractive outdoor activities. Therefore, an individual's
survey participation is possibly at least delayed. Thus, when the
weather encourages other leisure activities outside, it is likely that
invitees show low inclination to respond to the researchers'
request. As participation in a scientific survey is voluntary,
individuals are free to decide if and at what point in time they will
do so. In this respect, survey participation is a stochastic,
i.e. time-dependent, process \parencite{Singer2006}. In particular, an
online survey is a self-administered survey mode providing the invited
target persons with the opportunity to postpone starting to complete
the questionnaire to another suitable point in time. In case of ``fine
weather'', the participation can therefore easily be pushed to a day
with an ``unpleasant'' weather situation.

In sum, concerning individuals' deliberative cost-benefit calculations
regarding survey participation, it is assumed that---besides other
preferences, obligations, and alternatives---the weather situation and
the related alternative activities may function as incentives
diverting invitees from survey participation. Therefore, the
expectation is that a weather situation discouraging outdoor
activities, such as a cold and rainy day, results in immediate survey
participation and in a high participation rate. In contrast, a weather
situation encouraging outdoor activities, such as a sunny and warm
day, results in an individual's low inclination to participate in the
survey and thus in a low participation rate (Hypothesis 1). In this
sense, weather situations do not only affect the participation rate,
but also the individuals' timing of their participation: while an
``unpleasant'' weather situation is assumed to be associated with
``early'' responses to a request for survey participation, the
invitees retard their decision on survey participation in periods of
``pleasant'' weather situations (Hypothesis 2). As weather situations
partially correlate with the seasons, according to the finding by
\textcite{Goritz2014}, individuals are expected to be more likely to
participate in an online survey in winter than in other seasons
(Hypothesis 3). However, since weather situations vary within the
seasons, it is assumed that---net of the season---weather situations
being perceived as an adverse circumstance for outdoor activities are
correlated with a relatively high rate of early survey participation
(Hypothesis 4). It is worth noting that, to test these hypotheses, a
long-term panel study is needed, since multiple waves conducted at
different seasons and in varying weather situations are necessary.

The second theoretical approach often used for explaining survey
participation emphasizes heuristic and habitual decision-making in the
sense of traditional action \parencite[487]{Groves1992}. According to
this approach, to cognitively define the situation initiated by the
request for survey participation, bounded rational individuals make
use of short-cuts and ``rules of thumb'' in the form of cognitive
heuristics such as schemes, frames, scripts, and habits
\parencite{Esser1990, Simon1959}. On the one hand, given that
panellists have had positive experiences with previous survey
participation, have positive attitudes towards social-scientific
surveys, share an interest in the survey topic, accept norms of
reciprocity, show compliance with the legitimate authority conducting
the survey, and are convinced they are able to complete the
questionnaire without any effort, it is assumed they do not deliberate
on costs and benefits but make an automatic-spontaneous decision in
favour of the request \parencite[e.g.][]{Stocke2003}. On the other
hand, if invited target persons accept norms of reference groups that
demonstrate negative attitudes and values towards scientific surveys,
their swift refusal is often observed \parencite{Esser1986}. In sum,
according to this theoretical approach---in contrast with the above
formulated assumptions based on rational action theory---neither an
effect of the weather situation on the timing of response nor the
response rate would be expected. If invited target persons have
internalized the obligation to support the social sciences in line
with a value-rational action, the confirmation of related values
forces them to take part in the survey, mostly independent of any
season or weather situation. However, in cases of conflict between
different preferences, obligations, or unusual circumstances
concerning survey participation and alternative activities, heuristic
and habitual decision-making does not work. In these cases,
individuals are nevertheless likely to deliberate with some cognitive
effort the consequences of different alternative actions.

The question that now arises is which mechanism may be responsible for
the effect of weather and season on survey participation in the case
of automatic-spontaneous decision-making. \textcite{Goritz2014}, for
example, offers the ad hoc argument that moods induced by different
weather situations or seasons might have an effect on the target
person's decision to take part in the survey. Based on the
weather-mood hypothesis by \textcite{Watson2000}, this seems
plausible. In addition, \textcite[457]{Connolly2013}, reporting on the
responsiveness of wellbeing to climate and transitory weather
conditions, finds that life satisfaction decreases with the amount of
rain on the day of the interview and that low temperatures increase
happiness and reduce tiredness and stress. High temperatures, however,
reduce happiness, which is consistent with the fact that the survey
was conducted in summer. \textcite{Keller2005} also find an
association between weather and mood that is moderated by season and
time spent outside: ``pleasant'' weather (high temperature and
barometric pressure) is related to a better mood and better memory
during the spring as time spent outside increased.  They do not find
this relationship at other times of the year, but ``hotter'' weather
was associated with lower mood in the summertime
\parencite[724]{Keller2005}. Accounting for the findings by
\textcite{Potoski2015}, saying that surveys are at risk of
temperature-induced participation (particularly in the case of
indifference to survey participation), the association between weather
and survey participation can be assumed to be moderated by moods
induced by season and weather situations. However, a study by
\textcite{Schmiedeberg2014} reports, in contrast to a previous study
by\textcite{Kampfer2013}, a non-existent effect of weather situations
on answers to questions about life satisfaction.

Since the empirical findings on the weather-related mechanisms of
survey participation are mixed for theoretical and methodological
reasons, it is necessary to find other explanations. For example, it
is expected that obligations---such as reciprocity or
courtesy---initiated by the tailored prenotification or monetary
incentive prepaid by the researcher neutralize any seasonal and
meteorological effects on invitees' survey participation (Hypothesis
5). If individuals, in particular panellists having some experience
with such gifts given by researchers, accept internalized norms such
as social reciprocity, it is very likely that they will respond
habitually to gifts---such as unconditionally prepaid money---in terms
of a normative or norm-guided action if the selection of action could
be classified as being cognitive-emotionally under the control of a
social norm, such as accepted and legitimate reciprocity
\parencite{Weber1922}.  They follow this norm independently of
external influences, such as weather conditions or seasons
\parencite{Becker2019}.

According to the rational action approach, it is plausible that the
effect of weather situations on survey participation is moderated by
the regional opportunity structure (Hypothesis 6), meaning that the
regional opportunity structure is an initial precondition for
perceiving and realizing outdoor activities as an alternative to
taking part in the online survey. This means that the incentives by
weather situation become realized, providing there are opportunities
for activities in the living environment deterring individuals from
participation in a survey and that the benefits of these alternative
actions are larger than for survey participation.

\section{Data, variables, and statistical procedures}

\subsection{Data base}

The empirical analysis uses longitudinal data from DAB (Determinanten
der Ausbildungswahl und der Berufsbildungschancen) panel study
(\citeyear{DAB2020})---a multi-wave probability-based panel with a sequential
mixed-mode design \parencite{Becker2020a}.  The panellists are
adolescents born around 1997 and living in the German-speaking cantons
of Switzerland who have been interviewed mostly about their
educational and occupational trajectories after compulsory
schooling. The panel data is based on a random and 10 per cent
stratified gross sample of 296 school classes, out of a total universe
of 3,045 classes. A disproportional sampling of school classes from
different school types, as well as a proportional sampling of school
classes regarding the share of migrants within schools, were
applied. At school level, a simple random sample of school classes was
chosen. The initial probability sampling rests on data obtained from
the Swiss Federal Statistical Office (FSO) \parencite{Glauser2015}.

Between January 2012 and June 2020, eight waves were realized by
sequential mixed-mode surveys and the Tailored Design Methods
\parencite{Becker2020a, Dillman2014}. It was a push-to-web survey,
while withholding alternative answering modes was implemented
\parencites{Dillman2017}[76]{deLeeuw2018}[19]{Lynn2020}. Considering
costs and the participation rate, the first mode was a
computer-assisted web-based interview (CAWI); the second mode was a
computer-assisted telephone interview (CATI); and the third mode was a
paper-and-pencil interview (PAPI). In the case of the web survey, the
problem of undercoverage might be rather minor for this particular
sample of young panellists.  About 93 per cent of the Swiss population
has access to the internet and uses it basically every day, but each
of the interviewees of the DAB panel study (DAB = Determinanten der
Ausbildungswahl und der Berufsbildungschancen) had daily access to the
internet.

While in the first three waves interviews took place in the context of
the panellists' school classes, they have been followed since the
fourth wave (conducted in October and November 2014) after leaving
compulsory school. The fifth wave took place from June to August 2016,
Wave 6 from May to June 2017, Wave 7 in the same months one year
later, and Wave 8 was realized from May to June 2020. In each of the
waves (i.e. Waves 4 to 8) considered in this analysis, between 2,500
and 2,900 panellists were pushed to participate in the online
surveys. To improve the response rate, they got an unconditional
prepaid incentive (voucher, ballpoint pen, or a 10 Swiss Francs
banknote in cash) since they are effective for push-to-web surveys
\parencite{Becker2019, Singer2013, Goritz2008}. If one considers the
other survey modes as well, the total participation rate remained
rather constant at the level of about 80 per cent across the waves
(Table 1).

\input{7782_tab1}

In this study, the empirical analysis---limited to Waves 4 to 8---is
focused on the first mode of data collection (CAWI) only and, for
methodological reasons, the observation window is standardized to four
weeks---i.e. exactly 28 days \parencite{Becker2019}. For the five
waves (4 to 8), 13,220 spells were available for the analysis. Since
time stamps---collected automatically by the survey software
Unipark---indicate the exact time reference of the panellists starting
to complete the online questionnaire, it is possible to calculate the
exact duration of episodes from the start of the field period until
the start of participation on a daily or hourly basis
\parencite[e.g.][]{Durrant2013}. Furthermore, the spell data set
provides dynamic longitudinal estimations based on techniques of event
history data \parencite{Blossfeld2019, Becker2019, Becker2018,
  Allison2014, Rabe-Hesketh2012, Becker2011, Steele2008}.

\subsection{Statistical procedures and the dependent variable}

Since the time-dependent likelihood of participation in the CAWI of
the DAB panel study is the dependent variable, event history analysis
is an adequate statistical approach for estimating the distribution of
the waiting times from survey launch until the invitees' response. In
general, the participation rate is defined by the ratio of contactable
units and their response in terms of starting with the completion of
the online questionnaire \parencites[RR2 according
to][52]{AAPOR2015}[][11-12]{Bethlehem2011}[][637]{Singer2006}. Due to
the episode-oriented questionnaire on the young panellists' life
history, it is difficult to measure exact completion rates among
respondents. For data collection with an event history design, it is
uncertain if respondents completed the questionnaire or omitted some
of the episodes in their educational and occupational
trajectory. Given this uncertainty, about 80 per cent of the
respondents completed the questionnaire in the CAWI mode
\parencite{Becker2018}.

The aim of these statistical methods is the dynamic multi-level
analysis of longitudinal data regarding the occurrence and timing of
stochastic events, such as the eligible panellists starting the CAWI
depending on weather situation and other theoretically interesting
covariates. For estimating the time-dependent likelihood of survey
participation as a stochastic and time-variant function of individual
resources, survey settings, and exogenous factors such as the weather
situation, the hazard rate $r(t)$ is defined as the marginal value of
the conditional probability of the start of completing the
questionnaire in the web-based online survey in the time interval
$(t,t + \delta t)$, given that this event has not occurred before time
$t$ \parencites[29]{Blossfeld2019}[7]{Steele2008}. Using this
statistical procedure, it is possible to reveal causal impacts on the
occurrence of an event such as survey participation
\parencite{Becker2019}.

To consider the impact of time-varying covariates, such as changing
weather situations or the seasons in which the survey took place, the
technique of episode splitting is applied. This means that, for each
of the panellists, their initial waiting time is split into
sub-episodes on a daily basis. For each of these sub-episodes, a
constant hazard rate is assumed. Thus, the hazard rate will be
estimated on the basis of an exponential distribution:
$r(t|x(t)) = \exp(\beta'x(t))$, whereby $x(t)$ is the time-dependent
vector of exogenous variables whose unknown coefficients $\beta$ have
to be estimated. Based on the exponential model, it is possible to
model step functions that display the empirically observed hazard
function for the entire process until participation.

Employing the technique of episode splitting and the estimation of the
exponential mode, the statistical software package Stata (Version 16)
is used \parencite{Kohler2012}. The stsplit procedure is suited for
the episode splitting and the streg procedure for the dynamic
multi-level estimations \parencite{Blossfeld2019}.

\subsection{Independent variables}

The main exogenous variable at the macro level is the daily
information on the weather situation during the field periods of the
different survey waves. The following indicators measured on a daily
basis are considered: average air temperature by day (in degrees
centigrade); relative humidity (daily average in per cent); rainfall
(daily average in millimetres); duration of sunshine (in hours a day);
and barometric pressure (in hectopascals). These time-varying
indicators are taken from the SwissMeteo website of the Federal Office
of Meteorology and Climatology (\citeyear{MeteoSwiss2020}).

To reduce complexity and multicollinearity in the time series,
confirmatory factor analysis was applied to these four time series
separately for each wave \parencite{Harrington2009}. The factor was
extracted using the main component method and orthogonal factor
rotation. It explains almost 91 per cent of the variance in the
weather situation of October/November 2014, 90 per cent in May/June
2016, about 83 per cent in April/May 2017, almost 93 per cent in May
2018, and about 94 per cent of the variance in the weather situation
of May 2020. Figure 1 depicts the development of the weather
situation: the higher the factor scores, the higher the temperatures
and the longer the duration of sunshine. Lower factor scores indicate
uncomfortable weather---i.e. higher values for humidity and rainfall.


\begin{figure} \centering
  \includegraphics[width=\linewidth]{7782_fig1}
  \caption{Weather situations in the DAB field period across five
    waves}
\end{figure}


Furthermore, the different seasons in which the fieldwork took place
are considered using dummy variables. They differentiate between
spring (Waves 6--8), autumn (Wave 4), and summer (Wave 5), the latter
being the reference category. Alternatively, the panel waves (and the
prepaid incentives included) are captured by dummy variables.

\begin{figure} \centering
  \includegraphics[width=\linewidth]{7782_fig2} \caption{Distribution
    of the scaling variable representing regional opportunity
    structures} \end{figure}


The opportunity structure of the region in which the panellists live
is taken into account to consider competing factors possibly also
diverting the invitees from starting the questionnaire. From a
theoretical point of view, they are related to the panellists'
opportunity costs of survey participation. To account for regional
opportunity structures, macro-data from the FSO at regional levels are
used \parencite{Glauser2016}.

To indicate the regional opportunity structure, to reduce its
complexity, and to control the high correlation of the regional
contextual characteristics, factor scores were extracted from these
data. The total of 106 regions is characterized by a certain spatial
homogeneity, reflecting the principle of small, partially
cross-cantonal labour market areas with functional orientation towards
centred and peripheral opportunities and living standards in addition
to urbanicity, population density, and lack of social cohesion
\parencite[174]{Couper1996}. The distribution of the factor scores
across the German-speaking cantons is depicted in Figure 2
\parencite[20]{Glauser2016}.

To control social heterogeneity in the sample at the micro level,
different time-constant socio-demographic characteristics of the
panellists are considered. For one, this includes the panellists'
gender (reference category: male), as well as their social origin as a
proxy for the target persons' social context and economic resources,
social integration, and environment, as well as attitudes and values
in favour of survey participation
\parencites{Becker2019}{Stocke2004}[30]{Groves1998}[174]{Couper1996}. The
social origin is captured by the class scheme suggested by
\textcite{Erikson1992}.

Additionally, the interviewees' cognitive resources and language
proficiency---measured by their standardized grade point average in
German language---as a proxy for institutionally attested
language-speaking ability and intelligence, as well as the school type
in which they were enrolled, are included. They also indicate the
transaction costs and cognitive burden of survey participation. The
school type is also a proxy for educational level, correlated with the
appreciation of the utility of social-scientific research and
information-gathering activities \parencite[128]{Groves1998}.

Unobserved heterogeneity based on the reluctance of individuals to
start the questionnaire, on individuals' attitudes towards scientific
surveys, or on moods and emotions relating to the weather situation is
indicated by the panellists' latency between the invitation and
starting the questionnaire on a daily basis.

The descriptive statistics on the independent variables are documented
in Table A-1 in the appendix. They are calculated for the data set
with episode splitting.

\section{Empirical results} 

\subsection{Description of the timing of survey participation}

First, patterns of the timing of participation in the online surveys
are described. Figure 3 shows the cumulated hazard rates for the
different panel waves. It is obvious that panellists' responses were
more likely and occurred much earlier in Waves 6--8, conducted in the
years 2017, 2018, and 2020 during spring. In Waves 4 and 5, realized
in autumn 2014 and summer 2016, the hazard rates were much lower and
it took much more time for panellists to respond to the request to
start completing the online questionnaire.

The differences between the hazard rates for the three most recent
waves that took place in the spring months are significant. It still
has to be analysed whether these differences in hazard rates are
associated with the weather situation or with alternative explanatory
factors.


\begin{figure} \centering \includegraphics[width=\linewidth]{7782_fig3} \caption{Nelson-Aalen cumulative hazard estimates} \end{figure}


In the next step, the timing patterns of participation are analysed
explicitly regarding the season in which they took place. In Figure 4,
they are depicted as survivals curves. Again, the seasonal differences
in survey participation become obvious. For example, it was 11 days
before 50 per cent of the panellists invited to take part in the
spring waves (see reference lines) had actually taken part, while for
the other seasonal surveys there was no median value for the online
survey mode.


\begin{figure} \centering \includegraphics[width=\linewidth]{7782_fig4} \caption{Gompertz-Makeham distribution of survivals in terms of seasons} \end{figure}


After 28 days, 61 per cent of invitees had responded to the spring
surveys; in contrast, after the same amount of time, 46 per cent of
eligible panellists had taken part in the summer months and 45 per
cent in the autumn survey. While it took four days for a third of the
panellists in the spring surveys to start completing the online
questionnaire, just a quarter of them responded in the other seasons
over the same time interval. In sum, the timing and magnitude of
survey participation were significantly different depending on the
seasons usually providing different weather situations. For the online
mode, tests for the equality of survivor functions such as Log-rank or
Wilcoxon (Breslow) reveal that the survival curves were significantly
different for each of the stages in the field periods, each lasting
four weeks. The conclusion that these differences are strictly
seasonal has to be made cautiously, since the winter season is not
considered in this study.

\subsection{Impact of the weather situation on survey participation}

Utilizing a dynamic multivariate exponential model, the weather
situation is considered as a time-varying covariate (Table 2). Indeed,
there is a significant meteorological effect on the likelihood and
timing of survey participation.  In line with Hypothesis 1,
``unpleasant'' weather (cold and rainy) increases the likelihood of
participation, while the inclination for survey participation is much
lower during ``pleasant'' weather periods consisting of sunny and warm
days (Model 1).

\input{7782_tab2}

Indeed, in line with Hypothesis 2, ``pleasant'' weather periods result
in panellists postponing their response. An increase of one weather
factor score decreases the ``chance'' of participation by about 15 per
cent. This ``chance'' is calculated by subtracting one from the hazard
ratio $\exp(-0.167)$ and multiplying the result with 100 per cent.

This meteorological effect remains strong when other covariates are
controlled (Models 2--4). For example, it is expected that the
meteorological effect is associated with alternative outdoor
activities that are in turn associated with regional opportunity
structures. In line with Hypothesis 6, stating that the opportunity
structure is an initial precondition for perceiving and realizing
outdoor activities as an alternative to taking part in the online
survey, a significant effect of the regional opportunity structure on
survey participation is detected (Models 2--4). The higher the
urbanicity and living standard of the regional context of panellists,
the lower their inclination is to take part in the survey, even
despite the urban-rural divide of internet access. An increase of the
regional opportunity structure by one factor score lowers the
``chance'' of participation by about $(\exp(-0.047)-1) \cdot 100 = 5$
per cent. In general, this result is in line with other studies
revealing that the participation rates are higher in rural than in
metropolitan areas.

In addition, Hypothesis 6 is tested again by including the interaction
between the weather situation and the regional opportunity structure
(Figure 5a). While the main effects remain statistically significant,
the interaction between the macro-factors is insignificant. This means
that both the weather situation and the regional opportunity structure
provide independent influences on survey participation.

These macro-effects are constant when additionally accounting for the
prepaid incentives given to the panellists (Models 2 and
3). Therefore, Hypothesis 5, expecting that obligations---such as
reciprocity or courtesy---initiated by monetary incentives prepaid by
the researcher neutralize any seasonal and meteorological effects on
invitees' survey participation, is not confirmed. Independent of other
influences, cash as an incentive results in the earlier and higher
participation rates of panellists.


\begin{figure*} \centering
  \begin{minipage}[b]{0.49\linewidth}
    \subcaption{Opportunity structure}
    \includegraphics[width=\linewidth]{7782_fig5a}
  \end{minipage}
  \begin{minipage}[b]{0.49\linewidth}
    \subcaption{Seasons}
    \includegraphics[width=\linewidth]{7782_fig5b}
  \end{minipage}
  \caption{Effect of weather situations and \dots on survey participation ($\beta$-coefficients)} 
\end{figure*}



Furthermore, the effect of the weather situation remains significant
when the season in which the surveys took place is controlled (Model
4). Hypothesis 4, expecting that---net of the season---an
``unpleasant'' weather situation is correlated with a relatively high
rate of early survey participation, is also confirmed. It is worth
noting that the participation in a panel survey is most likely in
spring (see left panel in Figure 5b).

Hypothesis 4 is retested in an additional estimation since one could
expect an interaction effect of the weather situation and the season
on survey participation (Figure 5b). This interaction effect would
signify that the meteorological effect is different for different
seasons. This is indeed the case: on the one hand, the more
``pleasant'' the weather in spring compared to the weather in summer,
the less likely invitees are to take part in the online survey. On the
other hand, the more ``pleasant'' the weather is in autumn compared to
the weather in the summertime, the higher the participation rate in
autumn in contrast to summer.

Finally, it has to be emphasized that these macro-effects on survey
participation remain constant even after controlling the panellists'
characteristics (Models 3 and 4). The longer the panellists retard
their participation after the survey launch, the less likely they are
to start the questionnaire at a later point in time of the field
period. The more the socioeconomic resources (indicated by the
parental class position), the earlier and more likely the invitees are
to start completing the questionnaire. The higher their abilities and
achievements (measured by enrolment in a school type with a special
requirement and GPA indicating language proficiency), the higher their
inclination and speed of reaction to the request for survey
participation. In line with other studies, a gender difference is
found, confirming again that female panellists are more likely to take
part in surveys than their male counterparts
\parencite[e.g.][]{Keusch2015}.

Due to the coincidence of the coronavirus pandemic and the field
period in 2020, a direct COVID-19 pandemic effect, as well as an
indirect effect of non-pharmaceutical official orders and arrangements
related to the SARS-CoV-2 outbreak, resulting in the public shutdown,
on the survey participation in Wave 8 is considered by omitting this
survey (Model 5). Since the findings are stable instead of excluding
the most recent wave, the previous results are characterized to be
robust. However, possible COVID-19 pandemic effects on participation
in Wave 8 of the DAB panel study have to be analysed in detail
\parencite{Becker2020}.

\subsection{Characteristics of the weather situation and survey participation}

Finally, it is analysed which of the characteristics of the weather
situation are relevant for explaining the timing and rate of survey
participation (Table 3). On the one hand, panellists are more likely
to take part in the survey on rainy days: the heavier the rainfall,
the higher the pace and magnitude of participation (Models 1--4). An
increase in rainfall by one unit results in an increased survey
participation rate of $(\exp(0.295)-1) \cdot 100 = 34$ per cent. On
the other hand, ``pleasant'' weather characteristics result in lower
speed and a lower rate of participation: the longer the sun shines
during the day and the higher the air temperature, the relative
humidity, and the barometric pressure, the lower the survey
participation rate across the field period.

\input{7782_tab3}

The significant effects of the weather characteristics on survey
participation are valid, since the effects of panel waves remain
significant (Models 1 and 2). This means that meteorological effects
do not partial out the effects of the waves---i.e. they are no proxies
for impacts related to the waves, such as panellists' experience or
other unobserved heterogeneities. If one takes the seasons into
account, the effect of the weather characteristics (Models 3--4) and
the typical effect of seasons on survey participation (see Model 4 in
Table 3 and Figure 5b) are reproduced.

However, a closer look at the development of rainfall during the
different field periods (Figure 6) reveals that the effect of the
intensity of rainfall on both the timing and the rate of survey
participation depends on its timing within the field period. It makes
a difference whether heavy rainfall occurs at the initial stage of the
fieldwork or at later stages after survey launch.


\begin{figure} \centering \includegraphics[width=\linewidth]{7782_fig6} \caption{Development of rainfall in field periods} \end{figure}


Heavy rainfall at the initial stage is associated with swift
participation and high response rates; this is true for the field
periods in the three last waves realized during the spring of 2017,
2018, and 2020. There was no or less rainfall at the initial stage of
the waves conducted in autumn 2014 and summer 2016.


\begin{figure*} \centering
  \begin{minipage}[b]{0.49\linewidth}
    \subcaption{Seasons}
    \includegraphics[width=\linewidth]{7782_fig7a}
  \end{minipage}
  \begin{minipage}[b]{0.49\linewidth}
    \subcaption{Duration of field periods}
    \includegraphics[width=\linewidth]{7782_fig7b}
  \end{minipage}
  \caption{Interaction effects of rainfall in field periods and \dots ($\beta$-coefficients)} 
\end{figure*}

To make this observation watertight, Figure 7a shows the interaction
effect of rainfall and seasons on survey participation. Heavy rainfall
at a very early stage of the fieldwork contributes to higher
participation rates in spring and autumn. The magnitude of the
interaction effects of seasons and rainfall exceeds the main effects.


In addition, the interaction between rainfall and the duration of
fieldwork (in days since survey launch) provides support for the
importance of the timing of the rainfall. As depicted in Figure 7b,
rainfall is positively associated with survey participation, while the
increase in the participation rate significantly fades the longer the
field period lasts. The negative, but minor, interaction effect
confirms the assumption that the rainfall effect is largest in the
initial stage of the field period. Heavy rainfall around the survey
launch indeed works in favour of a high speed and rate of survey
participation.

Overall, these results are constant when an individual's social
origin, school type, achievement, and gender are additionally
accounted for (Model 2; not depicted). It is noteworthy that the
effect of opportunity structure on participation in the online survey
is still significant and negative (Models 1--4).

\section{Summary and conclusions}

The aim of this empirical study was to analyse how different weather
situations affect the inclination of panellists to participate in a
scientific online panel survey by controlling seasons, regional
opportunity structures, and individuals' resources and abilities. On
the one hand, this provides an indirect test of different theoretical
approaches seeking to explain why individuals participate in web-based
online surveys or refuse the request for response. On the other hand,
in the present dynamic longitudinal revealed preference analysis, the
focus lies on under-investigated time-dependent macro-level-impacts
(such as the weather situation, seasons, or the rural-urban divide) on
the timing of survey participation and response rate. The macro- and
micro-levels have been linked by connecting time series on weather
situations during the field periods of a multi-wave panel study and
event-oriented data on the panellists' participation in multiple
waves.

Applying techniques of event-history data analysis, the findings
indicate that ``pleasant'' weather situations have adverse effects on
the timing of survey participation, while ``unpleasant'' weather
situations result in early responses and high participation
rates. Furthermore, the earliest and highest participation rates were
observed during the spring months in contrast to summer and
autumn. These effects are not associated with the regional opportunity
structures providing opportunities for outdoor activities, possibly
diverting invited panellists from completing the online
questionnaire. The interactions between weather, seasons, and regional
opportunities were insignificant. However, there was an association
between weather situation and season. While in spring, the speed and
rate of survey participation developed positively during rainy and
cold periods, the panellists were more likely to take part in the
online survey during sunny and warm periods in the autumn
months. Furthermore, the results pointed to heavy rainfall at survey
launch being associated with high speed and rate of survey
participation. This is especially true for the spring period and---to
a lesser extent---for the autumn months. In sum, it is fair to say
that rather moderate weather situations are most efficient for
conducting an online survey in terms of rapid response and high
participation rates. For the management of web-based online surveys,
the recommendation is therefore to start the field period in times of
heavy rainfall if one is interested in high participation rates and
short field periods.

However, the peculiar development in Wave 8 realized in May 2020 could
be associated with the coronavirus pandemic of COVID-19, resulting in
the public shutdown specified by a governmental regulation declared on
13 March 2020 until 10 May 2020. If this public shutdown---organized
to avoid the spread of the infectious disease caused by
SARS-CoV-2---minimized the opportunities for outdoor activities, it
may have resulted in swift responses after the survey launch on 1 May
2020 and to the extraordinarily high participation rates, which have
to be investigated in detail (Figure 3).

In sum, the social mechanism behind the association between weather
situation and survey participation could not be revealed due to lack
of information. On the one hand, it seems plausible that a
``pleasant'' weather situation encourages outdoor activities, while
the start of completing an online questionnaire in a push-to-web
survey requires ``unpleasant'' weather. On the other hand, moods could
also be an important moderator for this association; but they are in
conflict with obligations initiated by pre-notification, prepaid
incentives, and respondents' attitudes to social-scientific
surveys. However, the essential precondition for an answer to this
open question is the analytical-empirical test of several approaches,
which attempts to deliver a mechanism-based explanation of survey
participation and unit non-response.


\section*{Acknowledgments}

The data of the first seven waves are available as Scientific Use
Files (SUF) at FORS in Lausanne and can be found in the online
catalogue under the reference number 10773.\footnote{DOI:
  \url{https://doi.org/10.23662/FORS-DS-946-4}} The SUF for Wave 8
will be available in 2021. The meta-data on field period, the time
series on weather situations as well as the data on regional
opportunity structures can be requested from the author. The data set
and syntax file is available on the website of SRM.

For her professional assistance in data acquisition and her comments
on an earlier draft, I would like to thank Nora J.  Moser.

For helpful comments on earlier drafts, I wish to thank the anonymous
reviewers and the associate editor of SRM.

\emph{Funding:} The DAB panel study is substantially financed by the
State Secretariat for Education, Research and Innovation (SERI).  The
interpretations and conclusions are those of the authors and do not
necessarily represent the views of the SERI.

\emph{Conflicts of Interest} The author declare no conflict of
interest.


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