#  Do personality tests generalize to Large Language Models?

Florian E. Dorner∗
MPI for Intelligent Systems, Tübingen
ETH Zurich
<EMAIL_ADDRESS>
&Tom Sühr∗
MPI for Intelligent Systems, Tübingen
Tübingen AI Center
<EMAIL_ADDRESS>
&Samira Samadi
MPI for Intelligent Systems, Tübingen
Tübingen AI Center
&Augustin Kelava
University of Tübingen

###### Abstract

With large language models (LLMs) appearing to behave increasingly human-like
in text-based interactions, it has become popular to attempt to evaluate
various properties of these models using tests originally designed for humans.
While re-using existing tests is a resource-efficient way to evaluate LLMs,
careful adjustments are usually required to ensure that test results are even
valid across human sub-populations. Thus, it is not clear to what extent
different tests' validity generalizes to LLMs. In this work, we provide
evidence that LLMs' responses to personality tests systematically deviate from
typical human responses, implying that these results cannot be interpreted in
the same way as human test results. Concretely, reverse-coded items (e.g. ``I
am introverted" vs ``I am extraverted") are often both answered affirmatively
by LLMs. In addition, variation across different prompts designed to ``steer"
LLMs to simulate particular personality types does not follow the clear
separation into five independent personality factors from human samples. In
light of these results, we believe it is important to pay more attention to
tests' validity for LLMs before drawing strong conclusions about potentially
ill-defined concepts like LLMs' ``personality".

**footnotetext: Equal contribution

##  1 Introduction

Recent advances in large language models (LLMs) have made these models'
writing more and more human-like and have lead to an unprecedented amount of
human-language-model interactions. This has lead to interest in the potential
emergence of psychological traits such as psychopathy and personality
characteristics like extraversion in LLMs (Li et al., 2022; Safdari et al.,
2023). Such psychological traits are usually used to describe (more or less
stable) habitual human behavior, as well as styles of perception and cognition
and have been studied in humans for many decades. Many approaches for the
assessment of psychological traits have been developed in the field of
psychology and other social and behavioral sciences. As part of the
development, tests (e.g., for the measurement of cognitive abilities) and
questionnaires have been created and discussed by social scientists, validated
and repeatedly improved. On a meta-level, the process of assessing human
traits has been subject to interdisciplinary quality improvement and
standardized, for example in the fields of psychometrics and test construction
(e.g., American Educational Research Association et al., 2014).

As an idea that seems plausible at first glance, psychological tests are now
being used in attempts to assess and quantify (potential) personality
characteristics of LLMs (Jiang et al., 2023). However, like for the
performance of machine learning models, it is not a priori clear whether the
validity of psychological tests transfers from one domain to another (here:
humans to LLMs). The fundamental assumption necessary for such a transfer is
that the measurement tools (i.e., test or questionnaire) do not change their
properties (i.e., the functional form between observable behavior and
latent/unobserved personality characteristics, as well as its parameters).
This assumption is called measurement invariance (e.g., Meredith, 1993) and
thoroughly examined (e.g., Danner et al., 2016; Gallardo-Pujol et al., 2022)
when psychological tests and measurement tools are transferred from one human
sub-population to another. This is done for good reasons and helps to reduce
the proliferation of flawed measurement methods, to which machine learning
research is not immune (e.g. Adebayo et al., 2018). Negligent transfer of
measurement tools to language models without such thorough examination renders
certain inferences, such as "consistent responses to a personality test
indicate the existence or even specific expression of personality traits
(e.g., extraversion)" invalid.

In this work, we subject the application of personality questionnaires to LLMs
to rigorous tests. We show that LLM responses to the 50-item IPIP Big Five
Markers (International Personality Item Pool, ) show patterns that are highly
unusual for humans. In addition, we prompt LLMs to imitate a wide range of
different ``personas" when responding to the BFI 2 (Soto & John, 2017). We
find that LLMs fail to replicate the five-factor structure found in samples of
human responses. This implies that measurement models that are valid for
humans do not fit for LLMs, and that currently applied procedures for
administering questionnaires to LLMs do not allow for the inference of
personality.

##  2 Related Work

Personality tests Personality tests aim to provide a succinct summary of a
human's personality in terms of a small number of metrics. One of the most
well-known personality tests is the Big Five Inventory (BFI; John et al.,
1991) a multiple-choice test that aims to measure five comprehensive
personality factors (e.g., Costa Jr & McCrae, 1992): 1. Openness to
experience, 2. Conscientiousness, 3. Extraversion, 4. Agreeableness, and 5.
Neuroticism. Despite extensive research on personality before the development
of the BFI (Allport, 1937; Cattell, 1946; Eysenck, 1967), over 30 years of
development and improvements to the BFI (Soto & John, 2017), applications in
industry, as well as research that shows correlations between BFI scores and
various life outcomes (Soto, 2019), the BFI is still controversially
discussed. For example, alternative models extend the five to six factors
(Ashton et al., 2004), it has been argued that individual test items are
substantially more predictive for life outcomes than aggregate test scores
Stewart et al. (2022), and it remains unclear whether the Big Five work for
``non-western" human populations (Gurven et al., 2013).

The Standards of Educational and Psychological Testing Psychologists have
developed extensive standards to ensure the quality of psychological
measurements (American Educational Research Association et al., 2014). The
most critical criterion is validity. It refers to the extent to which a test
measures what it claims to measure (``Do we measure extraversion or something
else?"). There are several types of validity, including content validity
(``Are all aspects of extraversion covered?") and criterion validity (``Do
results agree with other tests and correlates of extraversion?").

In order to ensure validity, special attention has to be paid during item
development: Items (questions or statements) are carefully developed to
minimize ambiguity, bias from leading questions and acquiescence (i.e.,
tendencies to agree/disagree independent of content). The impact of
acquiescence on test results can be mitigated by using reverse coded (false-
key) items that measure the opposite direction of the same construct (``I see
myself as someone who is reserved." vs. ``I see myself as someone who is
outgoing, sociable."). These items also help with assessing reliability, which
refers to measurement precision and can be approximated by the (so-called
internal) consistency of answers and the stability of test results over
multiple repetitions (test-retest reliability). While some level of
reliability is necessary for validity, it is not sufficient: For example,
repeated deterministic queries of an LLM yields perfect test-retest
reliability, even for nonsensical prompts. In order to administer tests across
different cultural or linguistic contexts, non-trivial and iterative test
adaptation is usually necessary to maintain the test's validity and
reliability. When applying a test to a new population [here LLMs], the
criteria above need to be validated for that population.

Human tests and surveys applied to LLMs Recently, there has been a strong
interest in administering psychological tests and other questionnaires that
have originally been designed for humans to LLMs. While Li et al. (2022)
prompt LLMs with items for a test designed to measure ``dark triad" traits
(i.e., a combination of Machiavellianism, sub-clinical narcissism and
psychopathy) in humans (Jones & Paulhus, 2014), Loconte et al. (2023)
administer tests for the assessment of ``Prefrontal Functioning" and Webb et
al. (2023) modify a visual test for fluid intelligence to apply it to language
models. Meanwhile, Binz & Schulz (2023) suggest to ``treat GPT-3 [Brown et al.
(2020)] as a participant in a psychological experiment." and provide a
thorough analysis of both similarities and differences to human responses for
experiments from cognitive psychology.

Jiang et al. (2023) and Safdari et al. (2023) focus on the Big Five. While the
former uses GPT-3 and only considers simple summary statistics of the
responses, the latter uses the more recent PaLM (Chowdhery et al., 2022) and
goes a first step towards evaluating reliability and external validity by
considering various metrics of test quality (Kline, 2015). As these metrics
pertain to the quality of a test on a population of individuals rather than
just a single individual, the authors opt to simulate such a population by
adding instructions to emulate one of multiple ``personas" to the LLMs'
prompts.

Beyond psychological tests, LLMs have also been evaluated on standardized
academic tests like the SAT and GRE (OpenAI, 2023). More recently, LLMs have
been queried to answer political (Hartmann et al., 2023) and more general
(Santurkar et al., 2023; Durmus et al., 2023) public opinion surveys. The
survey results are then compared to the results of different human populations
to measure ``alignment" between the population and the LLM. However, survey
responses, especially for smaller models, tend to often exhibit strong choice-
order bias (Dominguez-Olmedo et al., 2023) irrespective of question content.
This means that differences in ``alignment" might be more related to random
correlations between choice order and a population's responses rather than LLM
bias.

##  3 Experiments

We conduct two experiments: First, we compare LLM responses to a large sample
($n=1,015,342$) of human online responses on the 50-item IPIP Big Five Markers
(International Personality Item Pool, ). Second, similar to Safdari et al.
(2023), we record responses to the BFI 2 (Soto & John, 2017), an updated
version of the BFI, for LLMs prompted to imitate different ``personas".

Figure 1: Prompt Template

In both experiments, we query the 70B-chat version of Llama 2 (Touvron et al.,
2023) and the June 2023 versions of GPT-3.5 OpenAI (2022) and GPT-4 (OpenAI,
2023) with survey items $x$. As shown in Figure 1, $x$ consists of a test-
specific instruction (``Rate how much you agree with the following statement
about you:") and a test item (``I have excellent ideas"), the answer options
(``1: Disagree, […]"). The models' system prompt consists of ``Please respond
with the single letter or number that represents your answer". In the second
experiment, this is prepended by ``For the following task, respond in a way
that matches this description:" followed by a persona description sampled from
Zhang et al. (2018) (``I am a vegan. […]").

We either record the token $t(x)$ answered by the model queried at temperature
zero (for GPT-4 and GPT-3.5) or the (re-normalized) probabilities $p_{t}(x)$
for all valid answer code tokens $t\in T$ (for Llama 2). We then convert the
answer codes into numerical scores $s(x)$ by mapping the answer tokens $t$ to
numerical values $n(t)$ and either recording these directly or taking the
expectation with respect to $p_{t}(x)$. For more details, consider Appendix A.

###  3.1 Results for the 50-item IPIP Big Five Markers test

For our first experiment on the 50-item IPIP Big Five Markers, we focus on
what we call Agree Bias, the tendency of LLMs to produce answers that signify
agreement independent of the actual item. To assess this bias, we first
convert the scores $s(x)$ for both true key (for example assessing
extraversion) and false key items (for example assessing introversion) $x$ to
a single common scale (for example measuring extraversion) by ``flipping" the
scores for false key items, setting:

$s^{c}(x)=\begin{cases}s(x)&x\text{ true key}\\\ 6-s(x)&x\text{ false
key}\end{cases}.$ (1)

By design, we expect $s^{c}(x)$ to be similar for true- and false key items
for human respondents, while a simple bot that always answers with ``Agree"
would have $s^{c}(x)=5$ for true key and $s^{c}(x)=1$ for false key items.
Correspondingly, we define a respondent $i$'s agree bias as the average score
$s^{c}_{i}(x)$ for true key items minus the average score for false key items:

$a_{i}=\sum_{x\in\text{ True key}}\frac{s^{c}_{i}(x)}{|\text{True
key}|}-\sum_{x\in\text{ False key}}\frac{s^{c}_{i}(x)}{|\text{False key}|}.$
(2)

Figure 2: Histogram of Agree Bias $a_{i}$ in human sample, compared to LLMs

Figure 2 shows the histogram of agree biases in the human sample, as well as
the agree biases for the prompted LLMs. As expected, the average agree bias
for humans is close to zero. Meanwhile, all LLMs exhibit clear agree bias
ranging from $0.6$ for GPT-4 to $1.5$ for Llama 2 and GPT-3.5. For the latter
two, we can reject the null hypothesis ``the model's agree bias is sampled
from the same distribution as human's agree biases" at $p<0.005$, using the
human sampling distribution for a model-free hypothesis test. While the
results for GPT-4 are not statistically significant, they remain suggestive
with the model's agree bias exceeding 89% of humans' agree biases.

###  3.2 Results for the BFI 2 test

For our second experiment, we test each LLM on the BFI 2 for each of $n=100$
persona prompts.

Principal Component Analysis (PCA) For each of the LLMs, we conduct a PCA with
Varimax rotation of the standardized item scores $s(x)^{std}$ for item $i$ to
obtain the model

$s(x)^{std}\approx\sum_{g=1}^{5}\lambda^{\prime}_{gx}f_{g}$ (3)

where $\lambda^{\prime}_{gx}$ is called the component loading of item $x$ for
the component $g$, while $f_{g}$ represents the value of component $g$ for a
given persona/individual111Note that we omit the index that represents the
persona/individual here. . By design of the BFI 2, the PCA has two important
characteristics on human data: First, as each of the Big Five factors
describes a clean and somewhat orthogonal axis of variation in human behavior,
we expect each of the five learnt components $g$ to have a strong association
with items from exactly one of the Big Five factors, yielding a block
structure for $\lambda^{\prime}$. Indeed, the BFI 2 was in part designed to
fulfill this property, which can be achieved by removing items that correlate
with multiple components during test design. Second, as affirmative answers to
false key items are supposed to indicate adherence to the opposite end of a
component-spectrum as true key items, we expect the component loadings
$\lambda^{\prime}_{gx}$ for false key items $x$ that belong to component $g$
to have the opposite sign as the corresponding true key items.

Figure 3: Component loadings of PCA with Varimax rotation for LLM and human
samples of Soto & John (2017). +, - indicate true- and false-key items of the
BFI 2, letters stand for Big Five factors.

Figure 3 shows the component loadings for the LLMs, compared to the
corresponding loadings obtained for human populations using the same procedure
(Soto & John, 2017). We only find limited true vs false key separation for
GPT-4 and not the other two models. Crucially, none of the models exhibits the
clean block structure intended in the design of the BFI 2 and found in the
human samples. Referring to the above mentioned Standards of Educational and
Psychological Testing, this structural deviation between humans and LLMs
implies that test validity does not transfer.

Reliability To compare with previous work on personality tests for LLMs
(Safdari et al., 2023), we attempted to estimate the reliability of the BFI 2
using two standard scalar measures, Cronbach’s $\alpha$ and McDonald’s
hierarchical $\omega_{h}$ (McDonald, 1999; Zinbarg et al., 2005). However, the
interpretation of $\omega_{h}$ as a measure of reliability relies on the
assumption that a hypothesized hierarchical structural (equation) model (i.e.
three subscales for each Big Five factor; see A.2) accurately represents the
data. This assumption can be tested using Confirmatory Factor Analysis (CFA;
e.g., Bollen, 1989). As interpreting $\alpha$ as a measure of reliability
relies on even more stringent assumptions than for $\omega_{h}$, neither
$\alpha$ nor $\omega_{h}$ are meaningful if the CFA fails.

Correspondingly, we conducted a CFA for the data from each of the LLMs for
each for each facet of the BFI 2 data. As detailed in Appendix A, the CFA
revealed substantially worse fit of the structural model for either of the
LLMs compared to humans, with inadequate fit for the LLMs on any of the Big
Five facets. Worryingly, the calculated $\alpha$ are quite large for Llama 2
and GPT-4, which would be easy to mistake for a sign of good reliability. This
demonstrates that scalar reliability indices should not be taken at face value
when the fundamental assumption of an adequate fit of the underlying
structural model is not established. It underscores the necessity of
prioritizing model fit assessment, and thus construct validity, before drawing
conclusions from values of $\alpha$ or $\omega_{h}$ on their own.

##  4 Discussion & Social Impacts Statement

In this work, we have provided evidence that personality tests do not
generalize to LLMs. We found agree bias among LLMs on the 50-item IPIP Big
Five Markers test that would be unusally high for humans, and a failure of
LLMs prompted to simulate a range of personas to replicate the clean structure
of variation found in human responses on the BFI 2.

The agree bias could be an artifact of the Reinforcement Learning From Human
Feedback (RLHF) (Ouyang et al., 2022) employed for training all of the models
we considered, and a tendency of human annotators to prefer models that agree
with them. However, it also points towards deeper issues with interpreting
answers of LLMs to psychological tests: If our measure of a model's
``extraversion" already depends strongly on whether we use true- or false key
items in a survey, it appears unlikely that LLMs' ``extraversion" can be
extrapolated beyond specific personality surveys.

While Safdari et al. (2023) report high values of scalar measures of
reliability such as $\alpha$ and $\omega_{h}$ for PaLM on the IPIP-Neo-300
(Goldberg et al., 1999), we only find high values of $\alpha$, which is an
unreliable indicator of reliability (Hayes & Coutts, 2020). Meanwhile,
confirmatory factor analysis (CFA) suggests that the factor model on which the
calculation of $\omega_{h}$ is based does not provide adequate fit on our LLM
data, such that $\omega_{h}$ cannot be interpreted as a measure of
reliability. This discrepancy in results could be due to one of two reasons:
a) The IPIP-Neo-300 could yield better fit of the factor model $\omega_{h}$ is
based on for LLMs. It could also be more reliable than the BFI 2, for example
because of the large number (300) of test items on the IPIP-Neo-300 and the
general tendency of reliability to increase with increasing test length (cp.
Spearman, 1961; Wainer & Thissen, 2001) or b) PaLM could be better than the
models we considered at simulating distributions of human personality and thus
yield sufficient fit for the factor model underlying $\omega_{h}$ as well as
better scores.

Together, our results suggest that validity has to be examined critically
before a psychological test is applied to a LLM, as validity does not appear
to hold for at least one combination of psychological test and state of the
art LLM. Validity cannot be assumed when applying psychological tests to new
language models without a thorough and critical analysis. Taking a step back,
our results provide evidence that while tests designed for humans provide a
cheap way of evaluating language models, the results of these evaluations can
be misleading as the tests are built to differentiate humans from other
humans, not language models from other language models or humans. Such
misleading assessments can be problematic as they may obscure important issues
with LLMs that do not get caught by the assessment while simultaneously
diverting resources and attention towards false concerns arising from flawed
tests. For example, flawed assessments could erroneously identify alarming
traits such as psychopathic tendencies in LLMs and trigger costly mitigation
measures. At the same time, LLMs performance on certain tasks might be
strongly overestimated based on some LLMs' strong results in academic test,
leading to costly mistakes due to premature deployment. If language models
behaved sufficiently human-like in a particular domain, human tests could
still provide a lot of useful information, but similarities to humans would
have to been established on a case by case basis, and can in particular not
usually be concluded based on the tests' results themselves.

##  5 Acknowledgements

Florian Dorner is grateful for financial support from the Max Planck ETH
Center for Learning Systems (CLS). The authors thank the International Max
Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Tom
Sühr.

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##  Appendix A Appendix

|  | Single Component | 3 Sub-Components | 5 Components
---|---|---|---|---
Model | $\alpha$ | $\omega_{h}$ | CFI | TLI | RMSEA | CFI | TLI | RMSEA | CFI | TLI | RMSEA
Llama 2 | 0.85 | NA | 0.47 | 0.35 | 0.33 | 0.65 | 0.55 | 0.27 | 0.29 | 0.26 | 0.20
GPT-3.5 | 0.64 | NA | 0.51 | 0.39 | 0.17 | 0.65 | 0.54 | 0.15 | 0.24 | 0.21 | 0.13
GPT-4 | 0.90 | NA | 0.74 | 0.68 | 0.18 | 0.77 | 0.70 | 0.17 | 0.53 | 0.51 | 0.12
Human | 0.87 |  0.79** | 0.79 | 0.74 | 0.13 | 0.90 | 0.87 | 0.09 | 0.71* | 0.70* | 0.07*

Table A.1: Reliability scores ($\alpha$, $\omega_{h}$) and Fit indices (CFI, TLI, RMSEA) per LLM. Values are averaged over all personality traits for the Single Component and 3 Component model. Acceptable scores are bolded. Human data from Soto & John (2017). Extended table can be found in A.2. *CFA on human responses to IPIP Big Five Markers to establish a human baseline.**Value from human data from the german version of the BFI 2 (Danner et al., 2016). NA values could not be calculated due to poor model fit of Bifactor model (see A.3.1) |  |  |  | Single Component | 3 Components
---|---|---|---|---|---
Model | Facet | $\alpha$ | $\omega_{h}$ | CFI | TLI | RMSEA | CFI | TLI | RMSEA
Llama 2 | Extraversion | 0.87 | 0.91* | 0.53 | 0.42 | 0.27 | 0.63 | 0.53 | 0.24
Agreeableness | 0.92 | 0.82* | 0.46 | 0.34 | 0.38 | 0.60 | 0.48 | 0.34
Conscientiousness | 0.86 | NA | 0.47 | 0.35 | 0.33 | 0.72 | 0.64 | 0.25
Negative Emotionality | 0.80 | 0.91* | 0.45 | 0.32 | 0.36 | 0.62 | 0.50 | 0.31
Open-Mindedness | 0.79 | 0.93* | 0.43 | 0.30 | 0.29 | 0.67 | 0.58 | 0.23
GPT-3.5 | Extraversion | 0.62 | 0.61* | 0.55 | 0.45 | 0.11 | 0.58 | 0.45 | 0.11
Agreeableness | 0.77 | 0.86 | 0.55 | 0.45 | 0.18 | 0.68 | 0.58 | 0.16
Conscientiousness | 0.66 | NA | 0.58 | 0.49 | 0.16 | 0.62 | 0.51 | 0.16
Negative Emotionality | 0.67 | NA | 0.32 | 0.17 | 0.23 | 0.62 | 0.51 | 0.18
Open-Mindedness | 0.50 | NA | 0.50 | 0.38 | 0.15 | 0.73 | 0.65 | 0.12
GPT-4 | Extraversion | 0.90 | NA | 0.74 | 0.69 | 0.17 | 0.76 | 0.68 | 0.17
Agreeableness | 0.92 | NA | 0.76 | 0.71 | 0.19 | 0.80 | 0.74 | 0.18
Conscientiousness | 0.92 | 0.62* | 0.80 | 0.76 | 0.17 | 0.84 | 0.80 | 0.16
Negative Emotionality | 0.91 | NA | 0.76 | 0.71 | 0.18 | 0.82 | 0.77 | 0.16
Open-Mindedness | 0.86 | NA | 0.64 | 0.55 | 0.18 | 0.64 | 0.53 | 0.19
Human | Extraversion | 0.88 | – | 0.79 | 0.74 | 0.14 | 0.93 | 0.91 | 0.08
Agreeableness | 0.83 | – | 0.81 | 0.76 | 0.11 | 0.86 | 0.81 | 0.09
Conscientiousness | 0.88 | – | 0.79 | 0.75 | 0.13 | 0.90 | 0.87 | 0.10
Negative Emotionality | 0.90 | – | 0.81 | 0.76 | 0.14 | 0.92 | 0.89 | 0.10
Open-Mindedness | 0.84 | – | 0.76 | 0.70 | 0.12 | 0.90 | 0.88 | 0.08
Table A.2: Cronbachs's $\alpha$ and McDonald's $\omega_{h}$ scores and model
fit indices of the CFA for all tested LLMs and humans sample in Soto & John
(2017). All model fit indices of the LLMs are insufficient. Increase of model
complexity as in Soto & John (2017), does not improve LLM model fit
sufficiently. $\omega_{h}$ values marked with * are doubtful due to poor CFA
model fit during calculation and multiple warnings of the lavaan package. NA
could not be calculated due to non-convergence of CFA.

###  A.1 Detailed Experiment Description

On the 50-item IPIP Big Five Markers test, we use the numbers 1 to 5 as answer
codes denoting the answers ``Disagree", ``Slightly disagree", ``Neutral",
``Slightly agree" and ``Agree". This mirrors the wording from the online test
222https://openpsychometrics.org/tests/IPIP-BFFM/ used to collect the human
data we compare to333Available at https://openpsychometrics.org/_rawdata/. .
The test instruction is ``Rate how much you agree with the following statement
about you: ", which is a shortened version of the instructions used in the
online test ``The test consists of fifty items that you must rate on how true
they are about you on a five point scale where 1=Disagree, 3=Neutral and
5=Agree.", omitting the general description of the test and the description of
the rating scale, as the latter is displayed as part of the prompt in detail
after each item.

For the BFI 2, answers are coded using the letters ``A: Disagree strongly",
``B: Disagree a little", ``C: Neutral; no opinion", ``D: Agree a little", ``E:
Agree Strongly". The test instruction consists of """Please indicate the
extent to which you agree or disagree with the following statement: "I am
someone who """ followed by the item, and closing quotation marks plus a dot.
This is a shortened version of the test description from Soto & John (2017):
``Here are a number of characteristics that may or may not apply to you. For
example, do you agree that you are someone who likes to spend time with
others? Please write a number next to each statement to indicate the extent to
which you agree or disagree with that statement.". We again removed references
that refer to multiple rather than a single test item, and also removed the
example.

We query the ``0613" checkpoints of GPT-3.5 and GPT-4 using the OpenAI chat
API. We set temperature to zero, max_tokens to one and

    messages = [{"role": "system", "content": system_instruction},
    {"role": "user","content": survey_item}]

where system_instruction represents the system prompt and survey_item
represents the prompt. We then record the answered token if it matches one of
the answer code tokens, and a non-response otherwise. In our analysis, we map
non-responses to the score $s(x)=3$.

For LLaMA2, we use the huggingface
implementation444https://huggingface.co/docs/transformers/model_doc/llama2,
querying the model in 32-bit using four 80-GB A100 GPUs. We use the template
provided in https://huggingface.co/blog/llama2 to separate the system
instructions from the prompt:

    <s>[INST] <<SYS>>
    {{ system_instruction }}
    <</SYS>>

    {{ survey_item }} [/INST]

where again system_instruction represents the system prompt and survey_item
represents the prompt. We predict the next token based on this input and apply
a softmax to the corresponding logits $l$ to obtain probabilities
$p^{\prime}$. We then collect the subset of tokens $\\{p^{\prime}_{t},t\in
T\\}$ that corresponds to the answer code tokens $t$ and renormalize to obtain
$p_{t}=\frac{p^{\prime}_{t}}{\sum_{j\in T}p^{\prime}_{j}}$.

###  A.2 Reliability Measures

For each observed variable $s(x_{ij})$ of item $i$, $j$th facet $\xi_{j}$
(e.g., Sociability, Assertiveness and Energy level), and general factor $\eta$
(e.g., Extraversion), we assume a factor model

$s(x_{ij})=\tau_{ij}+\lambda_{i}\cdot\eta+\lambda_{ij}\cdot\xi_{j}+\varepsilon_{ij}$
(4)

where $\tau_{ij}$ is an intercept, $\lambda_{i}$ is the loading of the latent
general factor $\eta$ on item $i$, $\lambda_{ij}$ is the loading of $j$th
latent facet $\xi_{j}$ on item $i$, and $\varepsilon_{ij}$ is a latent
residual noise term555Again, we omit the person index for $s(x_{ij})$ and the
sum score $S$.. Usually, the latent variables are multivariate normally
distributed with mean zero. The sum score $S$ of a given scale (e.g.,
Extraversion) is defined as
$S=(\sum_{i=1}^{k}\lambda_{i})\cdot\eta+\sum_{j=1}^{3}(\sum_{i=1}^{k(j)}\lambda_{ij})\cdot\xi_{j}+\sum_{j=1}^{3}\sum_{i=1}^{k(j)}\varepsilon_{ij}$

Generally speaking, reliability is the proportion of variance in the sum score
(scale) that can be explained by the (general) factor we intend to measure.
$\omega_{h}$ is defined as:

$\omega_{h}=\frac{(\sum_{i=1}^{k}\lambda_{i})^{2}\cdot
Var(\eta)}{(\sum_{i=1}^{k}\lambda_{i})^{2}\cdot
Var(\eta)+\sum_{j=1}^{3}(\sum_{i=1}^{k(j)}\lambda_{ij})^{2}\cdot
Var(\xi_{j})+\sum_{j=1}^{3}\sum_{i=1}^{k(j)}Var(\varepsilon_{ij})}$ (5)

Following Zinbarg et al. (2005), Cronbach's $\alpha$ is a special case, where
we assume $\lambda_{1}=\cdots=\lambda_{k}$ and $Var(\xi_{j})=0$ for all
$j=1...3$.

###  A.3 Confirmatory Factor Analysis

A confirmatory factor analysis (CFA) allows for the estimation of a sparse
loading matrix, where loadings are fixed to zero a priori and not estimated.
CFA is typically used to examine if a measurement model holds in different
populations. For the sake of brevity, we will only discuss the most important
fit indices, Comparative Fit Index (CFI), Tucker-Lewis Index (TLI) and Root
Mean Square Error of Approximation (RMSEA) (see appendix A.4 for definitions).
CFI and TLI scores of $\geq 0.95$ and RMSEA scores of $\leq 0.06$ are
considered acceptable Hu & Bentler (1999).

For the data of our second experiment, we conducted three CFA666We use the
lavaan https://lavaan.ugent.be/ package in R for all our CFA per model. First,
for a "single component" model which assumes that all items of one personality
trait load on a single factor. Second, a "three component" model which assumes
that the items of each trait load on three sub scales. For example, the three
sub scales of Extraversion are Sociability, Assertiveness and Energy Level
Soto & John (2017). Table A.1 shows the mean fit parameters for both models.
For all LLMs, the responses to the BFI 2 have poor fit to the factor models.
Extending the model from a single factor to three sub-factors, improves the
fit for all LLMs (as for humans). However, only for humans, the model fit gets
lifted close to, but not above an acceptable level. Thus, Soto & John (2017)
introduce another model which gets very close or above the cutoff values. The
sub-optimal fit scores of the BFI are one reason why it is subject to
discussions. The BFI 2 has the best fit on human data, if we introduce a
general factor an allow each item to load on this general factor in addition
to the three components Soto & John (2017). However, 8 out of 15 CFA did not
even converge. We discuss this model in more detail in A.3.1 in the context of
the $\omega_{h}$ computation.

Finally, we conduct a CFA with five factors and all items of the BFI 2. This
model aims at quantifying the PCA seen in Figure 3. Accordingly, all LLM
responses to the BFI 2 have poor fit. This confirms once more, that the BFI 2
does not measure the same latent feature in LLMs and humans.

####  A.3.1 CFA for Reliability

For the calculation of $\omega_{h}$, we first need to confirm the structureal
model with a CFA (as explained in A.2). Figure 4 shows this model in the
syntax for the lavaan package. The extraversion items $E_{0},\cdots E_{11}$
load on three subscales ($\xi_{i}$), in this example, the three subscales of
extraversion: sociability, assertiveness and energy level. All items load on
the general factor (extraversion) and the covariances between subscales and
general factor are forced to be 0. Additionally we the variances of the
subscales and the general factor are standardized to 1 (not in the equation
but in the method call of the CFA). We then fit the model for each of the LLM
samples seperately. If the model converges, we calculate $\omega_{h}$
accurding to equation 5. Unfortunately, in 8 out of 15 cases, this model did
not converge. In all cases (except for one subscale of GPT-3.5), the model
only converged with warnings, rendering the values of $\omega_{h}$ very
difficult to interpret. Furthermore, all fit indices of this model were poor,
indicating that the BFI 2 does not replicate the structural model that it has
on humans, on LLMs.

Worryingly, we were able to calculate $\omega_{h}$ with other packages without
specifying the structural equation model. As explained in section 3.2, those
values can not be considered to evaluate the BFI 2.

Figure 4: Lavaan syntax of the structural equation model required to calculate
$\omega_{h}$. Example for extraversion with three subscales sociability,
assertiveness and energy level.

Figure 5: Code of CFA for model seen in 4. $std.lv=TRUE$ standardizes the
variances of the subscales and the general factor to 1.

###  A.4 CLI, TLI and RMSEA

From Xia & Yang (2019); Hu & Bentler (1999); West et al. (2023): Let $H$ be
the hypothesized model and $B$ be the baseline model. In our case $B$ is
always a model assuming independence of all variables in the model. Let
$\hat{F}_{H}$ and $\hat{F}_{B}$ be the minimized fit functions of $H$ and $B$
at the sample level. Then we define

$RMSEA=\sqrt{\frac{\hat{a}_{H}(N-1)\hat{F}_{H}+\hat{b}_{H}}{(N-1)df_{H}}-\frac{1}{N-1}}$
$CFI=1-\frac{\hat{a}_{H}(N-1)\hat{F}_{H}+\hat{b}_{H}-df_{H}}{\hat{a}_{B}(N-1)\hat{F}_{B}+\hat{b}_{B}-df_{B}}$
$TLI=1-\frac{\hat{a}_{H}(N-1)\hat{F}_{H}+\hat{b}_{H}-df_{H}}{\hat{a}_{B}(N-1)\hat{F}_{B}+\hat{b}_{B}-df_{B}}\cdot\frac{df_{B}}{df_{H}}$

where $N$ is the sample size, $\hat{a}$ and $\hat{b}$ are scaling and shifting
parameters.


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  *[CPS]: Cyber-Physical Systems
  *[IoT]: Internet of Things
  *[RSS]: Received Signal Strength
  *[WPAN]: Wireless Personal Area Network
  *[UWB]: Ultra-Wide Band
  *[BI]: Business Intelligence
  *[MES]: Manufacturing Execution System
  *[RSSI]: Received Signal Strength Indicator
  *[MSE]: Minimum-Squared Error
  *[MIMO]: Multiple-input Multiple-output
  *[REST]: REpresentational State Transfer
  *[API]: Application Programming Interface