Principate - Science topic

How do you think of this calculation?

I calculated after the principals of R=V, V=IR.

At the last, I finally reached at the principal, which E=I^{3}V.

I am conducting an Exploratory Factor Analysis (EFA) using Principal Axis Factoring with Promax rotation for the adaptation and validation of a scale. The scale consists of 60 items, and the original developer suggests five dimensions (although no factor analysis was conducted to establish these five dimensions in the original scale). To determine the number of factors to retain, I have performed the following procedures:

Can we evaluate these factor models using additional fit indices available in JASP? Specifically, can we use these fit indices to determine the optimal number of factors to retain in an EFA using the Principal Axis Factoring method? If so, which fit indices (e.g., RMSEA, SRMR, TLI, CFI, and BIC) would be the most accurate for deciding the optimal number of factors to retain?

A simple description and schematic ilustration of a cogeneration system based on a HT PEMFC for residential heating and domestic water usage

Trying to find out what are the leadership practices implemented by principals, especially those in primary education which encourage teacher job satisfaction

I need supporting and contrasting research done in the field of female leadership in education and the challenges female principals face in navigating leadership in High Schools.

Watch @ https://www.youtube.com/watch?v=aQolfkvYrM8

18 Sep 2024 at 10 AM Sri Lanka Time (04:30 Wednesday, GMT) 🚨

As artificial intelligence continues to advance, the future of software engineering is being reshaped. Many are asking, Will AI replace software engineers, or will it augment and transform the profession?

To address these important questions, we are hosting a panel discussion featuring industry experts who will share their insights on AI's impact on software engineering, productivity, and the evolution of skills in the field.

👥 Panelists:

What differences principal betwen DEVELOPMENT ECONOMICS and ECONOMICS DEVELOPMENT?

1. The purposed?

2. Indicator of betwen DEVELOPMENT ECONOMICS and ECONOMICS DEVELOPMENT.

3. Which importance betwen DEVELOPMENT ECONOMICS and ECONOMICS DEVELOPMENT for welfare society.

I am currently working on some plant species ISSR scoring data, which consists of 0s and 1s. I would like to perform a Principal Coordinates Analysis (PCoA) using GenAlEx. Could someone guide me on the correct input format and steps to accomplish this analysis?

Thank you

Qual o fator motivacional acerca da preparação dos professores, bem como ocorre a práxis educativa nas escolas. Em análise, o fazer educacional comtempla os ditames da educação contemporânea?

Transaction costs include all the costs associated with executing and governing a transaction. Since formal financial transactions are recorded in writing, and written records are the principal source of evidence in the case of disputes, people who can't read or write will avoid formal finance unless they receive their money first (as in the case of a loan, or a cash withdrawal).

"A governance structure is usefully thought of ... as an institutional framework in which the integrity of a transaction, or related set of transactions, is decided." [Oliver E Williamson]

When transactions fail to attain integrity, in the sense of a common agreement between the buyer and sell, markets fail. And in the case of microfinance, this means financial exclusion.

Hi,

I run an FE model on LS-DYNA solver, and concerning about the max principal strain contour result in HyperView. When I choose the result type as Strain(t)-Absolute Max Principal the contour seems to be very strange. I wonder if this result type is different from max principal strain, and what result type exactly i need to choose? Many thanks to any reply!

principal's information skill

- Would I happen to need an principal investigator conduct one?

Greetings and respect

I have done a non-linear analysis on a concrete water tower. It is important for me to know in which step and in which node the maximum of the first principal stress occurs.

Is there a way for the software, for example, for a 60-second analysis with a time step of 0.02, to automatically show the time of occurrence of the maximum of the first main stress, its location and its maximum value.

Is it correct to choose the principal components method in order to show the relationship of species with biotopes?

I am looking for an instrument to study the Sustainable Leadership (Andy Hargreaves's) of school Principals and its effect on Teachers' Productivity. I noticed quite several studies and research papers on the topic but, I am looking for anyone who has access or knowledge, and is willing to share any instrument that I can cite and use in my dissertation.

Thank you very much in advance.

Dear all,

I am trying to simulate the fatigue crack of aluminum in ABAQUS. I can't find the maximum principal stress of Al and other data that I showed in the attached file. Is there any solution?

#abaqus #fatigue_crack #maximum_principal_stress

Regarding the G20 summit, state-issued invitations sent to world leaders using the word “Bharat” have ignited rumours that the government might plan to phase out the English name India. In 1947, when British rule was finally overthrown, India ostensibly had three coexisting names, each with its own history, connotation and legitimacy.

There was India, a name thought to have its origins in Sanskrit, referring to the Indus River that runs through the north of the country.

There was Hindustan, the name used by the Persians, the Greeks, Delhi sultans and the Mughals for hundreds of years to refer to a large stretch of the north and centre of the subcontinent.

Finally there was Bharat, a name that is traced back to an ancient Sanskrit text, the Rig Veda – written around 1500BC – which mentions the Bharata clan as one of the principal tribes occupying an area now known as north India. It is also the name of a legendary king that appears in the Sanskrit epic the Mahabharata, who Hindus claim was the father of the Indian race.(https://www.theguardian.com/world/2023/sep/07/india-or-bharat-g20-invitations-throw-up-question-dating-back-centuries)

India, Hindustan or Bharat? What are your thoughts?

It is all in the question.

Thanks in advance.

Could customised-developed AI offer leadership and management support to Head of schools/Principals?

Une image d'un caractère manuscrit est une distribution de pixels dans un vecteur chaque pixel est une valeur comprise entre O et 255. Cette distribution peut être utilisée pour comprendre la répartition des données et en tirer des conclusions. La distribution de valeurs dans un vecteur peut être représentée en général sous forme de diagramme, d'histogramme ou d'autres types de graphiques. Ces graphiques permettent de visualiser la fréquence de chaque valeur dans le vecteur et d'identifier les valeurs qui se produisent le plus ou le moins souvent. Il existe plusieurs mesures statistiques qui peuvent être utilisées pour décrire la distribution de valeurs dans un vecteur notamment la moyenne, la médiane, l'écart-type et la variance. Ces mesures permettent de caractèriser la distribution de manière plus précise et de comparer les distributions de différents vecteurs. La méthode à utiliser dans une distribution de valeurs dans un vecteur peut être influencée par plusieurs facteurs, tels que la taille de l'échantilion, la nature des données ou la présence de valeurs aberrantes. C'est ce demier point qui consiste la problématique de cet artice. . Les méthodes statistiques sont généralement utilisées pour comparer la variance de plusieurs vecteurs de même type. L'explorations de ces nombreuses méthodes anciennes et récentes m'a conduit à tester l'utilisation de Principal Components Analesis combiné avec la distance de Mahalanobis PCA (analyse en composantes principales) est une technique qui permet de réduire la dimensionnalité d'un ensemble de données en transformant les variables d'origine en un nombre plus petit de variables non corrélées appelées composantes principales. La distance de Mahalanobis est une mesure de la distance entre un point et une distribution multidimensionnelle, qui tient compte des covariances entre les différentes variables. Autrement dit la distance de Mahalanobis est comme une seuil de distance entre un point et un groupe d'autres points pour identifier les points les plus éloignés ou inhabituels (données aberrantes (outliers)) ou pour déterminer si un point de données appartient à une distribution particulière (classification). Théoriquement l'application de PCA sur un ensemble d'images constituées de 28x28 (vecteur de 784 valeurs de pixels) réduira ces données à un nombre plus petit de variables, la distance Mahalanobis est appliquée sur les composantes principales pour identifier les images qui sont éloignées de la moyenne. si l'on trouve que l'image a une distance très élevée par rapport au centre de la distribution, cela peut indiquer que l'image est aberrante. Plus la distance de est grande, plus l'image est différente de l'ensemble de données. Le réajustement du seuil de distance utilisé est nécessaire en fonction des résultats pour identifier le seuil approprié. l'utilisation de ces méthodes statistiques sur des images de caractères manuscrit peut-elle donner de bons résultats en pratique?

I would like to understand the steps and commands involved in this process in STATA. I have tried few methods but nothing seems to be correct

I would like to construct principal components from 30+ financial ratios for a predictive model. I would then use logistic regression and support vector machines for the predictions, conditioned on the principal components. I have panel data with T << N. For PCA, the data should be iid. I am concerned that the time series are not independent. I have only 10 years of data, which precludes most time series statistical testing. I have seen several peer-reviewed papers constructing principal components using panel data, but the potential problems with using panel data for PCA are not discussed in the papers. The papers all seem to use the standard PCA approach one would normally use with a cross-section but with panel data. I have researched several means of doing a PCA with time series and a couple that use panel data as one of several examples of a general (usually very complicated) PCA procedure, but nothing seems to "fit the bill" for my standard panel dataset. I would greatly appreciate some direction as to where I might go to look for an adequate procedure or suggestions for a procedure that could possibly work. I am an applied econometrician, and it would be difficult for me to translate a complex procedure into code. So, ideally, I would like to find a procedure for which there is existing code (I use SAS and R). Thanks in advance for any insights provided,

please answer.

I recently received my doctorate degree. I am interested in collaborating with experienced researchers who conduct research on effective strategies in treating substance use disorders in those with mild and borderline intellectual disabilities. This was the title of my dissertation. I am interested in learning the full gamut of research principals on a grander scale.

According to the principal of entropy increase, it's easier to form more disordered crystal strcuture at low temperature. Do I mixed up the concepts of chaos and disorder?

Conceptualise organizational culture ?

I am currently working on a research about innovative management skills of Principals.

I am looking at how to reteach and intrinsically motivate a leader to teach this format style to their teachers. I am trying to create a how-to guide on this concept. Create something I can use as a manuscript and give to school principals.

I have a nonnegative square matrix A and a matrix B that is a principal submatrix of A. Is there anything I can say about how the eigenvalues of B are related to the eigenvalues of A? I'm not assuming that A is symmetric here.

-Rich

Anyone can kindly share a sample copy of (Principals Leadership Style) and (Teachers Job Performance) Questionnaires used in Parveen et al. 2022 study :Impact of Principal Leadership Styles on Teacher Job Performance: An Empirical Investigation or any other useful validated questionnaires. I'm looking at the impact of autocratic and democratic leadership styles on teachers performance. Thank you

Currently, I plan to take research about Floating Tidal Platform. But, I still confuse about the rules and optimization method for making new design of that platforms.

I am conducting an exploratory factor analysis and to determine the number of factors I used a paired analysis.

How can I generate the number of factors correctly in stata? Or other tool?

When using parallel analysis in stata, for example, if you proceed with Principal Axis Factoring all my Eigenvalues from the Parallel Analysis using a Principal Axis Factoring lower than 1. (Suggests in this case to retain all factors)

when out of curiosity, I use principal component factors, or even principal component analysis (I know this is not EFA), it suggests retaining 3 factors (which satisfies me)

Principal Leadership Programs

Pre-service Courses Outcomes

Higher Education

Student Engagement

How weights (WQI) derived from relative loads and eigenvalues ​​associated with water parameters in principal components (PCs) are calculated? I need help

RGPPM technique has been successfully expanded towards path planning for the delivery of merchandise during the last-mile. However, it is necessary to include indicators to measure fuel consumption and therefore the amount of carbon emissions. These indicators must be closely related to the carbon footprint caused by gasoline and electric vehicles.

Gusenbauer & Haddaway (2019) stated that Google Scholar is not appropriate as principal search system. As supplementary system, how should we use Google Scholar in relation to the principal search systems? Under what conditions can we use Google Scholar?

There are 3 leadership styles - autocratic, authoritarian, transformational with each having about 5 indices. I am the view that the appropriate tool should be the mode or the one that has the highest frequency after transforming each of the 5 indices in each of the 3 leadership styles to one single variable and then find the mode. But there has been diverse opinions that the one that has the highest weighted means will measure this.

I want to find the load at which a beam fails, so I want to plot a graph to be able to predict the failure load

Hello everyone, I applied PCA in python by taking lagged climate indices and then used its resulted two principal components (showing maximum variance) with GLDAS satellite data precipitation values in multiple linear regression to predict monthly precipitation. My data was 38 years monthly data. The correlation between GLDAS and model's predicted precipitation on the training set was 0.50 and on the test set was 0.49.

I wanted to check the model's performance further so I took 22 years monthly TRMM data and calculated PCA on 22 years monthly lagged climate indices. I entered the obtained two PC values in the previous developed multiple linear regression equation and acquired the predicted monthly precipitation. The correlation was calculated between the TRMM and model predicted precipitation which was negative -0.45.

What is the reason that I got negative correlation and what this negative correlation shows?

The SPSS tutorial says that Principal Component Method for factor extraction followed by varimax rotation. However, some of the experts suggest that it should be the Maximum Likelihood Method of Extraction followed by Promax rotation. Which is the right approach?

Hello, good morning everyone, i need to know the principal concepts that define the principal difference between the engineering investigation methodology and scientist investigation methodology. Thank you so much.

Hello,

To be sincere, I do not know if I can write this here, but I will try.

Some time ago, I have been working in order to understand and identify the drivers behind Land Concentration in Chile. Even though I have made progress, I am looking for a quantitative expert as a coauthor today.

The principal issue will elaborate an econometric model using the data collected.

If someone is interested just let me know.

All the best

I am interested in solving Delayed Differential Equation Systems with Runge-Kutta 4a. Order Method.

Based on the great reply of Dr. Ziaeemehrpost done in https://brian.discourse.group/t/adding-delay-differential-equation-solver/191/3 I did the same tentatives to solve the system used as example

dy0dt = -y0 + y1(t-1) + y1(t-10)

dy1dt = y0 + y1(t-1) - y1

dy2dt = y1 - y1(t-10)

with the RK4 method.

According to the example, I considered the system as a Python function

def model(y, t, n, h):

# dy0 = -y0(t) + y1(t-1) + y1(t-10)

# dy1 = y0(t) + y1(t-1) - y1(t)

# dy2 = y1(t) - y1(t-10)

y0 = -y[n][0] + y[n - int(1/h)][1] + y[n - int(10/h)][1]

y1 = y[n][0] + y[n - int(1/h)][1] - y[n][1]

y2 = y[n][1] - y[n - int(10/h)][1]

return np.asarray([y0, y1, y2])

where h is the integration step used.

The memory of the system was considered constant and equal to the vector (5, 0.1, 1) and declared with the function

def memory(t):

return np.array([5, 0.1, 1]),

and the knowledge of the solutions in the interval [-delay_max, 0] is performing the following Python function:

def history(func, t, y, t_start, delay_max):

for i in range(1,t_start+1):

aux = -(t_start-i)/float(t_start)*delay_max

t = np.vstack((t, aux))

for j in range(len(t)-1):

y_value = func(t[j])

y = np.vstack((y, y_value))

y = y[1::,:]

t = t[0:len(t)-1,:]

set_history = np.hstack((t,y))

return_history = []

for i in range(t_start):

return_history.append(set_history[i])

return return_history

This function returns the previous knowledge of the system in the interval [-10, 0] considering the discretization of this interval with step h, the same used in the integration with RK4.

My doubt is about how I must declare the values k2, k3, and k4 in the principal looping of the RK4 considering the respective increments k1/2, k2/2, and k3. I wrote the following function but I do not know how to declare these increments in my code:

# Numeric Solution

# Runge Kutta 4a. Order

def rk4(func, set_history, tf, h):

# Initial Time

ti = set_history[-1][0] + h

# Interactions to Looping of RK4 Method

iterations = int(np.floor((tf-ti)/h))

# Dimension of System (Time is Dimension, Too)

r = len(set_history)

dim = len(set_history[0])

# Inicialization of Numeric Solution Matrix yy

yy = np.vstack((set_history, np.zeros([iterations+1,dim])))

for i in range(r, r + iterations+1):

t_actual = yy[i-1,0]+h

k1 = h * np.asarray(func(set_history, set_history[i-1][0], i-1, h))

k2 = h * np.asarray(func(set_history, set_history[i-1][0], i-1, h))

k3 = h * np.asarray(func(set_history, set_history[i-1][0], i-1, h))

k4 = h * np.asarray(func(set_history, set_history[i-1][0], i-1, h))

aux = set_history[i-1][1::] + (k1 + 2*(k2 + k3) + k4) / 6

matrix = np.hstack((t_actual, aux))

set_history.append(matrix)

solution = set_history[r::,:]

return solution

Someone can help me? How must I declare the quantities k1, k2, k3, and k4 correctly?

Regards,

Magrini.

How can we calculate the sample size for principal component/ cluster analyses?

Dear all,

I performed a PCA analysis on a Likert scale with 5 questions which ordinal responses can be 1,2,3,4,5 and 6 (from strongly disagree to strongly agree). I did it in two independent samples. I obtained only one principal component in each group. Now I want to compare the principal component in each group. If my data were continuous, I know that the Principal components are continuous. However, as my Likert scale does not have continuous data (It can't), I would like to know if the resulting principal components should be considered continuous data or something else.

Of course, this is important to determine which test(s) should I use to determine if there is association between the two groups that I want to compare.

Very much thank you,

Nicole

Do you know any renowned article which has been published in Scopus journal describing that for conducting the Exploratory Factor Analysis (EFA), which method is the best, 'Principal component' or 'Principal Axis Factoring ' in SPSS?

I can understand the importance of having an outcome assessor independent and blinded of intervention for a Randomised Controlled Trial (RCT), but when conducting a Case Study investigating a new Clinical Health intervention is it also important to NOT allow the principal researcher to carry out baseline and post-intervention outcome scales/measures?

My understanding is that the principal objective of a Case Study is to establish the feasibility of a new intervention rather than effectiveness and more importantly ensure that the participant does not experience any adverse effects. Because of this, the significance of any non-feasibility scales are minimal so for this reason would it be a poor design for the principal researcher to undertake the outcome scales/measures?

Thank you for your advice regarding this question!

Ken

currently i am working on steel connection using abaqus (quasi static analysis) .i applied the pretension force by thermal load on shank . the problems as followed :

1. is it right to make trial and error till reach ur required pretension force , since the principal calculations didn't give the required temperature .

2. Total energy increased too much during preloading step , and keeped with same high value during loading step , did i miss something .

Thank you

A friend of mine is conducting a study on "Principals' managerial skills and School effectiveness". The dependent variable of the study is school effectiveness. The researcher intends to find out whether the following managerial skills - Communication, decision-making, and supervisory skills correlate with school effectiveness. School effectiveness was measured as a product of teachers', students' and administrators' effectiveness. For considering teachers, students, and principals themselves in the dependent variable, the researcher states that the "population of his study comprised 810 school leaders (270 principals and 540 principals), 2,5763 teachers and 13,890 students. From this population, 10 per cent each of principals, teachers and students were selected at random for the study. Is there anything wrong with the population? A lecturer who is not even the supervisor said it's wrong, but I felt he was right since teachers, students and school administrators are taking part in the study. The lecturer said the population has to be unitary, and as such, all the secondary schools should rather be used.

The idea of this lecturer about population choice has affected many students' theses. Thus, I decided to bring this topic here up to get the opinions of other experts regarding the choice of population.

To obtain the moment of inertia values of my compounds, I performed calculation using gaussian 09 program (B3LYP/6-31+G(d) level of theory). In the log file, however, the values I want to obtain was replaced with asterisks as follows.

------------------------------------------------------------------------------------------

Principal axes and moments of inertia in atomic units:

1 2 3

Eigenvalues -- 1444.27032********************

X 1.00000 -0.00018 0.00173

Y 0.00022 0.99970 -0.02455

Z -0.00172 0.02455 0.99970

------------------------------------------------------------------------------------------

Is there any way to display the missing numbers?

Evaluation of Spatial-Temporal Variability of Drought Events in Iran Using Palmer Drought Severity Index and Its Principal Factors (through 1951-2005)

See Table 2 for a published example of PDSI and soil moisture.

1.If we have many principal components (eg more than 5), all having eigen values more than one. Can we reduce the data in to two principal components intentionally?

2. Can we consider a variable as independent if it has strong loadings on two or more than two components?

Mindfulness is included in 3º therapy generations, but maybe the Principal MBI instructors (or MBSR, MBCT) are using a cognitive model.

Principal Component Analysis (PCA) is a multivariate statistical technique to reduce the volume of the large dataset with minimum loss of information and identified the major components along with which maximum variance associated. Generally, PCA was performed using varimax rotation with Kaiser Normalization. The output of the analysis is expressed in terms of Principal Components, their % variance, and factor loading of the variable. In practice, the values of factor loading greater than 0.6 are considered as significant variables. Many times, the values of factor loading are lesser than 0.4. What does it mean? How the result to be interpreted in this case having lower factor loading?

Anyone who has an idea about the difference between Principal Research Scientist and Senior Research Scientist can share with us for getting more understanding for this research journey.

I am working on hourly multivariate time series, due to the huge dimensionality of the data, I convert the data into functional data, using the Fourier basis function, the model use in this problem is the functional autoregressive model of order more than one, as per my knowledge their is no package available in R to deal with such model. So I use the alternative, I decompose the functional curve through spectral decomposition into functional principle components function and there associated scores. Then using the multivairiate time series method to forecast the principal components scores, then multiple these forecast scores with functional principle components functions to retransform to functional form from multivarite, In this a way I obtain one year a head forecast, where each day is a single curve. Know my problem start from here that I want to check the accuracy of the model, I think that I evaluate each curve into 24 points, but how to due this is in R. when I obtain these forecasted values in which each day of 24 hours, compare it with origional hourly data, and calculate the mean absolute percentage error, please help me.

What should be the role of a High School Principal? Whether He /She should be a good manager or He /She should be a good leader? A good manager often fails to be a good leader.

How can I calculate multiple linear regression(MLR) from absolute component scores(APCS)?

How can I calculate the Contribution (%) table?

please guide me

I have a project to evidence Thomas Robert Malthus theory about a principal of population (Malthusian Spectre/Malthusian Trap). I want to attest, his theory about a relationship of population and earth production/environment. is that applied in a country that i would like to attest or not? But i was confused, what variable that i can use to analyze it empirically?

Buenas tardes,

Necesito incluir el siguiente título en la titulación de mi perfil principal y no aparece en el desplegable, ¿Cómo puedo realizar dicho cambio?

Muchas gracia de antemano.

Un saludo,

Elena Cuevas

When searching "cobalt" in google, some of the results that appears are azurite minerals. I know that cobalt production mainly comes as a byproduct from copper or nickel production but haven't found any direct relation between azurite-cobalt. So, my question is, what copper or nickel mineral is the principal for cobalt production, if there is any?

Entre mi alumnado me encuentro con un alumno con problemas cognitivos donde no es capaz de expresar emociones ni gestionarla y me gustaria encontrar articulos y recursos para poder tratar con el con el uso de las tecnologias como elemento principal y asi poder ayudarlo.

One of the principal objects of restorative justice is focussing the restoration. Although debate about the subject matters of restoration is not recent, it has been continuing since 1970s. What is your thought about it?

Let’s suppose, how does the principal of secondary schools manage teaching resources for quality learning in his/her school?– is the basic research query and I wish to look at how the practice evolved over the past 20 years. What could be its steps, any helpful software, techniques, or any suggestions would be highly appreciated. Thanks.

Hello all,

Early next year I'm planning to evaluate a training for school principals. I will collect data from school principals with experience (what that entails is to be defined, but they should be in the field for X amount of years), who have been in that program. I'm currently thinking of a questionnaire (big sample), followed by interviews with some interesting individuals (also to be defined). At the moment I'm not sure yet how I would do that or what specifically I would ask, so any ideas are welcome. If you think of something else than a questionnaire or an interview, please do share. I am wide open to suggestions.

Dear colleagues,

I am conducting my EFA in SPSS, using principal axis factoring and oblique rotation.

Is there any rule of thumb when a certain percentage of nonredundant residuals is too much?

I would be greatful if you could point out some articles/sources to me where this issues has been discussed or even solved.

Many thanks

Marcel

While creating a wealth index using the household asset (dichotomized ), Can we take the second principal component (comp 2) if it has more relative positive eigenvectors (For example: as shown in the attached picture)? If yes, which is the best reference to quote. Thank you

Researching school principal development models in Australia

I am using Principal Component Analysis (PCA) to create an index required for my research. My question is how I should create a single index by using the retained principal components calculated through PCA. For instance, I decided to retain 3 principal components after using PCA and I computed scores for these 3 principal components. What is the appropriate ways to create, for each respondent, a single index out of these 3 scores?

• Is it relevant to add the 3 computed scores to have a composite value?

• Or to average the 3 scores to have such a value? • Or should I just keep the first principal component (the strongest) only and use its score as the index?

Alternatively, one could use Factor Analysis (FA) but the same question remains: how to create a single or overall index based on several factor scores?

Any advice, or documentation will do.

I wish to use the principal coordinates of MCA as input variables for cluster analysis.

What are the stress evaluation required for a FEA study on dental implants

Principal Leadership Programs

Pre-service Courses Outcomes

Higher Education

Student Engagement

I am wondering whether there is any relevant literature on how to best estimate the sample size of a hypothetical clinical trial with various treatment effects (10%, 20%, 30%) based on the scores of the first principal component in a PCA. The scores summarize changes of various markers over time which are standardised and which are associated with clinical outcome measures.

Many thanks in advance