Γεια σας, είναι Vicky εδώ και ευχαριστώ για την συμβαίναση μου σήμερα. Μερικές χρόνια πριν είχα είχα ήρθει ένα συμβαίνασμα για το Ζέμουσα Σταμβλόγ, όπου είχα κάνει ένα εξαιρετικό λαϊόνι. Και όταν δεν είχα δει αυτό το βίντεο, εγώ είμαι σχέσης σήμερα στο κανάλι μου. Και για το σχέδιο σήμερα, κάνουμε ένα τεχνικό τεκνικό. Σήμερα θα χρησιμοποιήσω ένα σχέδιο για να δημιουργήσω το σχέδιο μου και αν θέλουμε να είμαστε ξου gene π債σ φτιάξευνες, θα σας δείξω πώς πρέπει να δείξω το σχέδιο σήμερα στο σχέδιο σας. Σετάκτυπο θα σας πρέπει να μη διαχώ τον πλαίτι, και μετά θα σας χρησιμοποιήσω μία αναφαρμή, και θα παράξω το συμβαίνασμα στο φωτοφαρμό σου. Αλλά θα σας χρησιμοποιήσω ένα σχέδιο, στον αυτον με αυτό το σχέδιο μου, και θα θα δείξω ότι θα θα χρησιμοποιώ έναν μερικές εξαιρετικές, Εντάξει απ' αυτό το σπινό μου. Και Just because today I want to play with color I am going with vibrant colors from the Dilution's collection. I'm going to start with lemon zest and squeezed orange. I am going to use a spatula and apply a little bit of paint directly on my plate. Then I'm going to use my brayer to mix the colors, but you will see that I'm not trying to mix them up and create a brand new color. Θα ήθελα να έχω τα όμορφα σε όμορφα μου. Και τώρα μπορώ να χρησιμοποιήσω μια σκέφτα και σκέφτα βραδικά στο μπροστά μου. Παρακτήσω πώς μπορώ να τα παίρνω πάνω με ένας κομμάτις. Δεν είμαι τελειώσο με το κλείο με την σκέφτα και αυτός μπορώ να το παίρνω πάνω μετά με έννοια να κάνω ένα σκέφτα σε τα μάχα μου. Λοιπόν, όσο όπως βλέπεις σκέφτα στον παιδί σου, μπορείτε να πω να αυθώ και πάνω και πάνω. finishing duration and remaining time. The last thing is here to do as in painting I have to finish off in this way but I will finish off my paint in a few moments until your plate is pretty much clean. Jelly printing is a great way to create interesting results on your Argenal background and there are so many techniques to use it it's really fun and I just wanted to show today Αυτή είναι η λόγια σου. Μπορείς να το κάνεις και να το κάνεις πιο ενδιαφέρον. Λοιπόν, θα κάνω ένας στένσλικο τέτοιμπο σπίτι μου. Θα χρησιμοποιήσω αυτήνης καλύτερη ρότα. Αυτή είναι η ρότα της πόστας ρότα από διλούσια. Θα σπρετεύω με το σπίτι μου και θα χρησιμοποιήσω ένας από τα στένσλια. Αυτό είναι τα στένσλια από φαβρικαστέλ. Και θα πω ένα σπίτι. Και τώρα η σπίτι μου έχει έναν καλύτερο συγγραμμό. Αυτό θα ας ζητούστω αντιμετωπικά στον μας εταί εμπραγματική καλύτερη ρότα. Και μπορείς ναSee that I'm getting some interesting results. Μπορείς να κάνεις άστονο με αυτήνης καλύτερη ρότα. Επομένως που δεν μπορείς να χρησιμοποιήσεις δυσκλήρωση από τα στένσλια που όχιζες στένσλια ή με πρωτοφασίστικες κογόδρες. Αλλά θα ας ζητούσα εδώ και μπορείς να δείτε ότι θα χρησιμοποιήσεις απόα μου το μυαλήμα μεταγράφω κάτω τοολογιδό. but I'm making sure that I keep that beautiful design from the stencil and the blending of colors and you can make it as busy as you want. I decided to stop here because I'm going to do a lot of things on top and I don't want to have too busy with the background. Now one of the things that I love about the jelly plate is what stays on top of the plate once you pull off one print. So you will see what I mean. I'm going to use some scrap paper here and pull off one print but what stays here is a beautiful texture to add on your pages. So I'm going to do that as a finishing touch with my jelly plate and if you think that this is a messy process think about it again, it's not messy at all and you can see that I am actually cleaning my jelly plate and my breaker on top of my page and everything is clean now. Now all you have to do is to use a baby wipe over this plate and the breaker and they are ready to store. So now to add a little bit of texture on my background I'm going to use this stamp by Dilusion's. Since I went with Dilusion's paints I decided to go with Dilusion's stamps as well. I'm stamping at the background with Archival ink which is permanent and I am using Orange Blossom. So it's very close to the colors that I have at the background and this is going to create a nice subtle background. And here is a closer look to both those pages and now I'm going to use a black marker and draw a frame. I always like to have a frame on my pages. I think they give a nice finishing touch. So I'm free hunting this border and then I'm going to use a black marker and color outside of this line. The black on the frame is going to help the inside of my page to pop even more at the end.  I think that going all over with a black marker is the quickest way. Now with a thin brush I'm going just outside that frame that I have drawn and I'm using this paint by Dilusion's to draw one more line. It doesn't have to be perfect. Remember this is Archival ink. So I'm going to go all around it and this is going to be a vine where leaves and flowers come out from. You will see what I mean later on.  This is the finishing touch for my background and I want to have a little bit of white at the back because I always use my white gel pen to add highlights on my focal points and this is going to help everything come together at the end. And this is where the inspiration for this page came out from. These are two gorgeous stamp sets by Stampendou's and when I see big bold designs such as those sunflowers I always think of my art journal and how I can use them there. So I'm going to stamp everything with black Archival ink.   You can see what I mean here. No border just outside those black lines. So now I'm going to stick everything down on my page for doing so I'm using my matte medium by Ranger. I'm going to decide where everything is going to go and stick everything down. As I'm sticking the things down I'm going to make sure that I go over them with gel medium and this is going to ensure that every one of those little images are non porous so I can color them later on by using my big brush markers. And again now with my thin brush I'm using fresh lime which is the exact same color as the one I used for the border and I'm going to draw the stems for the flowers as well as for all those little leaves as if they are coming out from the border. And as I am doing that just to remind you that that's all always you can find the full list of all the supplies that I'm using today including color names and everything else down below in the description area as well as on the blog. So after sticking everything down and connecting those leaves with the vine I'm using my white gel pen to add some interest on the border. So you see that I am drawing some lines I am dividing that black area into sections and with a white marker I'm going to color in some of them white and you end up with a striking border and I really love how this comes out.  You see how easy it is to blend the color just because I have covered everything with gel medium. The surface is non porous so I can easily move the ink around. This ink is indian ink and it dries permanent but before it dries you do have a few minutes to move the ink around and do the blending. Of course you can use your favorite coloring method to do all these but when I am working on my art genre I don't care about having everything perfect like Copica coloring perfect so I just go ahead and do that with my finger it gives me a lot of pleasure. I am going to go back over the leaves with a darker marker now to add some shading and then I am going to go again on each one of those leaves down at the tips of those leaves and by using this shading technique with my big brush markers you can see how the leaves do not end up looking flat you can tell which leaf is in front of which one and it really gives a nice dimension on my page. I am adding a little bit of shading on the stems and now that I have finished with my green color I am going to go ahead and use a thin black pen and I am going to define the lines and now for coloring the sunflowers I am using again the same technique that I used for my leaves I am applying first the lightest color which is yellow and then I am going to add a slightly darker color to add the shading again I am just touching the marker and blending out the color with my finger and to deepen the shading even more I am going to add a touch of brown and for the last part of my sunflower I am playing with my browns so again I am using three different shades of brown starting with the lightest color and going to the middle one and to the darkest and blending everything out with my finger and don't be afraid to use really dark colors for your shading they really add a great dimension on your projects another one of my go-to techniques is to use a darker marker and create some shadows all around those images that I have stacked down on my pages and this is going to help them pop even more against the background I am using my white gel pen over those images and I am adding some highlights on the leaves and on the sunflowers and I really love the look of it just make sure that all the ink and the paint is totally dry before you use this pen and it's going to write beautifully and now I will stamp to add my quote for that I am going to create your own sunshine and I am using this alphabet stamp set by my favorite things and these letters are specifically designed so when you stamp them you can connect one letter to the next one and the final result is just beautiful and I am stamping my quote with black archival ink now I can go on and on with my finishing touches so when my quote was there you can see how beautiful it looks I am using my white gel pen to add a highlight on each and every letter this is going to help my quote pop even more against the background and to finish it off I am also going to use my nouveau drops and I am going to add some dots here and there all over my pages because this is going to add a whimsical touch on my layout and I am also going to add some dots at the centers of my sunflowers and now all that's left to do is to add the date and that was the art journal for today I hope you had fun and got inspired don't forget to leave me a comment and here are some close up photos of the project Thank you all for watching


Let me tell you this. Do you know what lost media is? No, I'm asking those to the people who is new to this kind of subject. Lost media is media that doesn't exist anymore, or something that is no longer available to the public. This includes TV shows, movies, videos, music, books, games and much more. However I've heard countless stories of people experiencing certain lost media. And I do in fact have a lost media experience as well. One time I used to watch a lost version of Ratatouille that depicted two scenes I only remember before I found it. One scene was that of Emily getting killed by being struck by lightning, and a scene of a bird's eye view of a deceased person at a kitchen, due to the fact that somebody accidentally puts poison in his food. I like to call a first person view a bird's eye view because why not? In the view, people are fighting with the sounds of underwater, and the vision was blurry. The words, no heaven, no hell, appears on the screen. Note, I was at school that time, and what I saw just disturbs me. I get the fact that it was a movie, but something wasn't right about it. I have in fact found the movie, I was on a hunt for it for a while now. I just regret watching for a reason. It just feels too horrible to even take a look at it. Why would I see Emily die from getting hit by lightning? Why would I see a bird's eye of a deceased person? It doesn't feel too right. I remember watching many traumatic films and shows too, such as Elfenlide, an anime not for kids. Basically I did find the movie, but I absolutely regret watching it. It's too realistic for a cartoony fashion film. No heaven, no hell, being put onto the screen just makes me uncomfortable. I've seen experiences from people watching dark and disturbing Lost Episodes that contain disturbing and horrific scenes of violence and much more. But before I mention the origin of Lost Episodes, let me tell you a few experiences from some users online. The first user was a male, who lives in Chicago, and had an experience of a Lost Episode of the TV show, Care Bears. This Lost Episode focused on some of the Care Bears going to defeat No Heart. This Lost Episode started to get dark when No Heart transformed into a line and devoured one of the Care Bears to death. Of course no blood, but he was screaming in absolute pain. The user doesn't remember who that Care Bear was. Some users actually have seen this episode before. Some of them were traumatized from viewing this specific Lost Episode from the Care Bears series. Care Bears showed has other Darker Lost Episodes as well. But my experience was only viewed by few. Not a lot of people have seen the Lost Ratatouille film. Someone has the similar experience with me, and apparently before the hunk finished, he said that he has in fact seen this alternative version of Ratatouille that was never supposed to air at all. This alternative version of Ratatouille was something Pixar shouldn't be ever allowed in their films. And like I said, I'll explain later. The next user shared his experience with the Lost Episode of Scooby Doo, where Shady and the gang investigate a haunted hotel with some creepy paintings inside. While the investigation was still going, Shady sees something odd. Apparently there was an arm reaching out from the painting, and grabbing Shady straight in, trapping him for the rest of his own life, right in that painting. The episode ended there. So basically why do people make these episodes and films into Dark Lost versions of themselves? I need to find out, and I need to debunk if some of the user's experiences with Lost Episodes are real or fake. From the following, who have been saying they've encountered these Lost Episodes? Yet I have the Lost Ratatouille film, however I need to go on a scavenger for Lost Episodes to see if they are real, and why the creators made these Lost Episodes to begin with. Such as some users saying they have seen a Lost Episode of the Three Stooges, where Curly ate his hand off in that episode. They have been saying he was hungry, and wanted to eat himself in that very specific episode of the Three Stooges. And then there was this episode of King of the Hill, where Hank actually gets injured, while getting into a car crash while being drunk. So basically I need to go somewhere, where there's pretty much an explanation on why Lost Episodes exist in the first place. So therefore I went to California to ask Disney about this Ratatouille film. Okay, apparently today I've learned about this Ratatouille film. Disney told me about the actual origins of Lost Episodes, and why they exist. They followed us to some sort of vault containing episodes, films, games, music, advertisements, books and audio recordings that have been lost to this day. But why are they kept locked in shelves inside a vault? It's confirmed that any company has this kind of lost media marketed for themselves, and the production teams surrounding the show or film. Apparently they made separate private adult episodes for themselves to view and not released on air. These types of media include dark humor, disturbing elements, drugs and much more. Why do these people, who created such shows like SpongeBob SquarePants The Simpsons or something like that, to include adult themes or supposed dark humor to be added to their own sakes? Each director or production team are too interested in the show at times, and create episodes for themselves to enjoy that includes disturbing elements or supposed dark humor into them. Some of the production team members have different tastes of humor. Whether it's got to be strange or edgy, the creators will always follow their advice for themselves to enjoy.  Something you weren't allowed to put on film, until like in the 1960s or the 1970s. I ask some of the members if they found an anime series similar to Elf and Lide. They said that there is a lost scene where Lucy gets a strange nightmare, and their company isn't for companies who made Elf and Lide. I know that scene before, but I'm not interested to yet, and I found a ratatouille film three years ago. But the members did show us some lost episodes of cartoons. They showed us the first lost episode, which is an episode of The Muppets Show, where Kermit is actually seen with a coat, and walks to a bar. He drinks beer in this lost episode, and talks to Gonzo about sex. The scene continues on, until Kermit gets his face deformed into something unusual and really strange. It's probably because of him drinking too much, but he wasn't drunk. His face looked to be different and some of it was rotting away. The episode then ended there. I told them about a lost Mickey Mouse short, about Mickey dying from tear gas on accident. He didn't have a gas mask on whatsoever, so he unfortunately dies from gas. The scene cuts two vultures feeding on his body, and it's nothing but bones. I told them about where I would go to find that Scooby-Doo lost episode, however I needed to go to Warner Brothers, that's surprisingly close to the Disney production headquarters. But before that, I saw that one ratatouille film, that I regretted to watch since three years ago. But I have somebody with me to watch this film. But I couldn't, I asked him about it, and lead me to a room. Oh god, why was I there?  When the film began, my heart began to race for this film. Emily dies, and at the end was a bird's eye view of a deceased person.  It indicates death, and that's why I absolutely regret watching this ratatouille movie for three years. I got out and drove to Warner Brothers to find these different lost episodes of specific shows. It was a few towns away but I luckily made it. When I arrived, I met some of the people there, and it wasn't too bad. But they didn't have a vault that contains lost episodes. Surprisingly, they managed to get a few lost episodes and films from companies as well. The reason why they were there is because the companies sometimes trade different and separate episodes from different shows to keep for themselves to enjoy. Our next one was a lost episode of The Amazing World of Gumball, a show that was silly and pretty quirky if you ask me. But that's what I'm not talking about. This episode was titled, Gumball's Soul. In this lost episode, it started with Gumball talking to Darwin about meeting with a person who they had never met before. They grabbed their stuff and met this random person. This person was written in a cartoon style as usual. But here's something that gets dark. He shows his hand and takes Gumball's soul to hell. It wasn't too messed up, but why would Gumball ever take his soul to hell? That's strange and unerving if you ask me. The next one is a lost version of the movie Beetlejuice. This movie shows one of the characters throwing up on what appears to be a baby mixed with some sort of fish and a lizard. Okay, that was some very weird stuff in Beetlejuice. What is the point of throwing up on a weird looking baby in this version of the movie? Then we got some music album of what appears to be a lost song sung by the Red Army Choir. I played the song and it actually contains lyrics about the gulags in the Soviet Union and how it affected many people. One part of the lyrics was the Berlin Wall and how a boy died on his birthday after trying to get a ball across the wall. Pretty heavy stuff, eh? The last item on the list was a lost episode of Looney Tunes. The episode was called Bugs Bunny's Injury. The episode began with Bugs messing with Elmer Fudd. It seems like your normal Looney Tunes episode, but all of a sudden, a bottle gets flying right towards Bugs Bunny's arm. He gets multiple cuts on his arm, and for some reason, he puts something that looks like lemonade onto his arm and screams in pain and agony. The reason for that is really unknown, but it's pretty painful and gruesome if you ask me.  What was the point of Disney making a realistic portrayal of life in Ratatouille? The fact they had a part, where there's literally a first person, bird's eye, view of a corpse with the words, no heaven, no hell, plastered to it. Disney is a happy company, not some truth teller. Now it just angered me thinking about death after that film. I always feel like I'm gonna get killed for some reason, it doesn't feel safe. What is the point of a film so beloved by many, to have an altered version of itself including a first person, bird's eye, view of a corpse? Why do they have to add in the words, no heaven, no hell, in? And why are there other experiences of other dark lost episodes? But anyway, I actually found what appears to be a lost cassette tape, of what appears to be an interview of something lost. I put the cassette tape into the player, and played the audio recording of what appears to be an interview. The interview played like this. A production team member is getting interviewed by another person for a lost episode. The tape went like this. So, explain to us about hidden material in the entertainment industry? Yeah, that's for ourselves and we make them private. Please ask permission to see them first. Okay, can we see them? Okay, here is one of them, a lost episode of the Twilight Zone. I warn you, it contains graphic scenes. When he puts this whatever thing in, the episode sounds like it was about a man, who was living in some house, where he finds some aliens by his yard. He greeted them and they greeted him. However things go dark. In the audio, I hear the sounds of bone crunching and screaming from the man, along with what sounds like a cruel experiment on him, so he can become an alien. The episode ended there. The interview continues on with this. So what was the point of making separate private episodes and films, while your job was supposed to make these films and TV shows for showing others? Here's the thing, it's the fact that there are some weird members of whatever crew there is. Especially from companies such as Warner Brothers, Disney or something like that. Some people have some weird sense of humor. It's nothing too special. Why were these films made? Because the director can achieve any private idea they want for themselves. They can allow dark humor, violence and maybe even some realistic elements to that as well. I was about to get off from that recording, until I heard the word, Ratatouille. One staff team member wanted a much more realistic way of some sort of film. However he needed to work at Pixar still, and asked the director advice for some realistic effects on the characters. It's nothing humor related. So he thinks that this lost version of Ratatouille should have realistic portrayals. Yup. Exactly, why would the director make and follow something like this? It's like a movie production's free time. They have these vaults that contains lost episodes or versions of certain films, shows, music, games, advertisements, books, audio recordings and even paintings. They pretty much like to keep them as their own. You know how like certain kids shows or films are marketed towards kids? Yes. That's because some of the members aren't into them. They also wanted films and episodes marketed towards themselves. They keep these episodes and alternative versions of movies and vaults, and maybe even bring them home with them. I stopped listening to the lost interview between the truth behind lost episodes. That's how lost episodes are made, but the question is, why do they sometimes make them public to some viewers? Basically I was thinking of going to go ask some local team member on phone, or something like that for the fact that they sometimes appear to some people at different junctures. I just don't know why, so I decided to find some local phone number from somebody, who is a part of one of these companies running films and shows. So I grabbed a phone book to see if there's any person I can contact to. But before that, what I had in thought was the Care Bears Lost episode to debunk whether it's real or not. But I did ask one of the team members at Warner Brothers to deliver me a box set of DVDs of lost films and episodes. It featured films and shows such as Cats and Dogs, Space Jam, Animaniacs, Looney Tunes, and other films and shows that aren't a part of Warner Brothers, like Rocko's Modern Life, Beavis and Butthead, Good Burner, Beverly Hill Cops, and of course, Elphin Lithe. When the box set was delivered, I got these films. But, there was a lost episode of Courage the Cowardly Dog that actually got into me. The episode was titled, Courage is kidnapped, which just sounds plain awful enough. Courage the Cowardly Dog was my beloved childhood character. I wasn't to it, but at the same time, I just don't want my childhood character to have a horrendous fate. I saw Courage as a loving character that inspired me to watch Courage the Cowardly Dog, and I wasn't into watching it. Oh God, I'm absolutely traumatized now. After watching the Courage the Cowardly Dog episode, I think I will never see Courage the same way again. The episode started with Muriel and Houston's talking, until Courage goes outside.  It is absolutely horrific, and the way he was kept as a slave, and was almost starved to death disturbs me. I won't go in full detail on it. It's just too horrific, it's nothing really sexual assault related, or something like that, but he was tortured in a graphic way that I can't explain.  Luckily he survived from those horrors. I found a member, who works for Cartoon Network, on a phone book. His name was Brian, and I had to call him about these secrets behind these certain lost episodes. I tried calling him a couple of times, but he wouldn't answer. It took me a while when he began to call, and when he did, I asked him about these lost episodes being viewed by some people. He responds. Oh, how did people manage to get our lost episodes you may ask? I'm assuming there is some group of hackers putting our lost episodes in stores, some production members are actually parents, who brought their lost episodes to their houses. Sometimes kids would find these lost episodes of shows and alternative versions of films on accident, thinking that those were normal.  It's unfortunate, but it's true that those kinds of people are doing this. Now I can see why these episodes are getting found by specific people. But there is one thing I need to do, to find the lost episode of Care Bears, where no heart mauled one of the bears alive. Then there was another phone number, for somebody who worked at Pixar. So maybe I could know much more of the lost ratatouille film, that featured realistic things that could happen in real life, such as Emily getting killed by lightning, or the view of a deceased person. Yet I'll say this again, I call first person viewing as birds eye viewing. It's probably because I'm a kind of confusing person. I called this next person at Pixar about the film. First said, so lots more to this than the film itself. Rather than the bird's eye view of a deceased person. He laughed and said, So who calls a first person angle a bird's eye view? But anyway, yes there is more to it. Apparently our members made an alternative version of this film, days after when the public ratatouille film was made. However what I noticed was that when he sounded somewhat like Padden Oswald, at the same time he really doesn't. I told him, who voiced Wemmy in the alternative version? He responds with, Somebody else, who I think is named, Gary Shandling. He voiced Wemmy in this alternative version of ratatouille. The call continued on. I said, so why did you pick Shandling instead of Oswald? I knew he was gonna respond. I have no idea, but he just sounded like him. I asked him another question. Have you worked at Mill Creek Entertainment? He said, I have before, are you looking for something? I responded, a Lost Care Bears episode, where no hearts devoured one of the bears. He said, I don't know if that exists. I didn't know of all containing lost media of any kind during that time. However I am aware there could be a lost episode of the Care Bears series with no heart in it. The call ended, so I asked another person about this Care Bears Lost episode. One day however, I heard somebody chatting with another person in a hotel, containing the words, an episode of Care Bears I found. So I asked this person and told what the episode was about. So you want to see your childhood ruined? Okay, apparently no heart transformed into a wild animal, and devoured Champ Bear. I wanted to see it, and therefore they led me to their room. They have the DVD. Oh God, I'm pretty nervous to see Champ Bear getting horrifically devoured to pieces by no heart. It's not exciting, but I'm gonna watch it. When the episode began, my heart raced. It raced, and raced, when the episode continued, until it stopped when they get to no heart. He transformed into a lion, and mauled Champ Bear into shreds.  I stopped watching that episode, it wasn't good to see Champ Bear getting brutally mauled to death by no heart. It wasn't fun, the episode was real. It was real and it was horrific. After a few days later, I somewhat calmed down from the ratatouille film, and the Lost episodes of Courage the Cowardly Dog and Care Bears. Thanks to the people and thanks to that one audio recording, now you know why Lost episodes exist. That's pretty much the end of the story, I don't have much more to say to you, than the fact that people kept Lost versions of mainstream media for themselves.


This is the second presentation of my introduction to latent transition analysis. In the first presentation I highlighted that latent transition analysis is a person-centered approach applied to repeated measures and longitudinal data. So it allows to identify the categories of individuals that make up a sample at different points and how those categories can explain the patterns of behaviors we observe at different time points. But also allows to investigate the structural relationships between those latent categories, those latent classes. So how individuals may change or not across development and across time and how they may transition from one category of behavior to another. In this second presentation I will provide more details on how to conduct latent transition analysis and I will follow this outline which I have taken from a chapter I published in the paper linked here. I will cover the first three stages of this outline focusing particularly on issues concerning the selection and specification of measurement models for each age or each time point of data collection. So I will start with a similar example of fictional data that I provided before where we asked adolescents to report the frequent use of these substances when they were age 14 years and again when they were age 15 years of age. I will emphasize here that in these and other examples I referred to categorical indicators in this case dichotomous variables. However, latent class analysis and latent transition analysis can be easily applied to any type of indicators from nominal to count data to continuous variables. So we have collected this data over two time points so we will observe associations between the indicators and the associations will involve associations between the indicators at each time point and longitudinal associations between the same indicators at different ages. The first stage of latent transition analysis is to find person-centered measurement models at each time point. That is, latent classes that can explain the viability of behavior patterns at each time point. So for this reason we start by looking for the best latent class models at each time point separately. And to indicate this separation here I have added a gray line that divides the two time points. So latent class analysis allows to select the number of latent classes and the line subgroups that can explain the viability behaviors we observe in the sample. And if you want to learn more about latent class analysis, please see my resources for NCRM. Not here that when I introduced the latent classes, the associations between indicators disappeared. This is to represent the key assumptions of latent class analysis, that of conditional independence. This assumes that the indicators are independent conditionally on latent class membership. That is, what explains the associations between observed behavior is the underlying latent class. So let's assume in this example that I identified two classes, one of substance use experimenters and one of substance use abstainers. And I just want to remind that latent class models will provide these parameters. Firstly, the item response conditional probabilities, that is the probability indicated by P to report a type of behavior in one indicator. For example, alcohol use conditional on latent class membership. For example, the probability of reporting use of alcohol for people in the experimental class and so on. And in the outputs, these probabilities will be reported in tables like this one, where we see the probabilities of answering different ways to the different items for people in different classes. Note that by inspecting these probabilities, we can interpret the meaning of the latent classes. For example, we see that individuals in latent class one have higher probabilities of reporting alcohol and cannabis use. And those in latent class two have low probabilities of reporting use of these substances. The other parameters provided by latent class analysis are the prevalence of the latent classes. So, how many individuals are likely to be in latent class one and in latent class two. And note that these are probabilistic. In fact, latent class analysis also provides the posterior probabilities of latent class membership. That is, for each individual in the sample, latent class models estimate the probability that that individual belongs to latent class one or latent class two. So, an individual is assigned to a latent class with uncertainty. For example, in the table here, you can see that individual 103 is assigned with latent class two, but this assignment is very uncertain compared to others. And latent class models vary in the degree of uncertainty. Some models may provide classifications that are more certain and precise, but not perfect. And the statistic entropy provides a measure of the classification precision. Entropy varies from zero to one, where one indicates a certain classification. So, spotlight on age 15 now. And I assume that at this stage there is more variability in behavior patterns we observe. Therefore, we might identify an additional class of substance users that of abusers. And how should we decide the number of latent classes and the line behavior patterns at each time point. And there are a number of statistics we can use. And I talked about this in my resources on latent class analysis. The main point is that, similarly to structural equation modeling, there isn't a single statistic we can use. So, we need to consider different statistics and different indicators. For example, statistics that compare the actual distribution with the distribution associated with the latent class model. We can use information criteria to decide which is the optimal latent class model. And we can consider entropy. And it's also important that we consider theory and substantive knowledge to check the plausibility of the solutions, latent class solutions we identify. But one important point concerning latent transition analysis is that since there are different statistics to consider and often they don't agree on the best model, it is always advisable at this stage of latent transition analysis to consider a pool of plausible models to be investigated in other stages of latent transition analysis. So, the selection of latent class models at each time point may be informed by how these models perform in other stages of the analysis. So, when we are applying measurement models to different time points, we may also consider tests of measurement invariance of these models. So, let's consider a simplified example here. And I assume that there are two underlying classes that explain the observed partinal behavior at age 14 and age 15 years. These classes also appear similar, they seem to have the same meaning and I've called them a class of experimenters and a class of abstainers. We can regress the latent classes at age 15 on those at age 14 using multinomial regressions. However, since the two classes are appearing or appear to be similar, can we plausibly assume that they have the same measurement parameters at both time points? And the measurement parameters in latent class analysis are the item response conditional probabilities. In this example, we can see that they are not the same, but both two classes at each time point represent individuals that in latent class 1 report higher probabilities to use substances and in latent class 2 report low probabilities of not using substances. So, the question is, can we assume that these differences may be trivial and therefore assume that the associations between latent classes and the indicators are the same across time points? For example, can we constrain the conditional probability of reporting alcohol use for someone in latent class 1 to be the same at age 14 and age 15? And similarly, can we constrain the conditional probability of reporting alcohol use for those in latent class 2 to be the same at age 14 and age 15 years? So, we can impose these equality constraints and test whether those are plausible, whether those assumptions or those constraints are plausible. So, once I have imposed these constraints, the conditional item response probabilities are the same across time. And this model with equality constraints is attractive because first we need to estimate fewer parameters once we constrain measurement parameters to be the same across ages. And second, this also facilitates interpretation of the model because the latent classes have the same meaning. But it's a similar model with equality constraints plausible. Since the model with equality constraints is nested within the model where measurement parameters are freely estimated, we can compare the two models using a likelihood ratio test, which will provide a formal test of the null hypothesis that the two models provide the same fit. And in the exercise and the additional material to these resources, I provide more example of how to run this test. So, here I'm providing a more complex example where at age 15 identified an additional latent class. But still we might consider plausible tests of measurement invariance if we identified classes that are similar across time. For example, I may identify a class of abstainers. And interesting testing whether the measurement parameters of these abstainers are the same at age 14 and age 15. So, it's possible to test measurements, to test models where there is partial measurement invariance across time, or at least measurement invariance for classes that appear to be similar across time. But because there are many different models of partial measurement invariance, it's important that those tests and those models, the definition of these models are also guided by theory and substantive knowledge. Now, the first stage is to extract latent classes parameters. And the first stage is basically taking the measurement parameters from the latent class models selected for each time point and then investigate the association between the latent classes and change across time. So, the question is, then why do we need to do this? Why cannot we jump to investigate in the associations between latent classes while at the same time estimating the measurement models? But the reason why it might not be advisable to do so is can be glimst by considering what happens if we also added a distal outcome to the model. For example, here education attainment at age 16 years. If we estimate the latent class models at the same time as the structural association between the latent classes and the regression of the distal outcome on latent class at age 15, the latent class model at age 15 is represented not just the covariance of the force systems in the use indicators, but also the covariance of the distal outcome with the age 15 indicators. So, this means that while we may intend the latent class model to explain associations between the substance use indicators, the model is actually explaining the associations between indicators and educational attainment. Or in other words, by including a distal outcome, the model changes because the latent class at age 15 is also taking into account other covariances. And this poses theoretical problems in interpreting the latent classes and practical problems when we add the distal outcome, the measurement model of the latent class measurement model at age 15 will change its parameters. And the same problem arises when we include covariance in the latent class and the latent transition models. So, it may not be advisable to estimate the measurement model in parallel with the structural relationships because problems arise as soon as other variables are included. And this problem includes substantive problems in interpreting what we are actually measuring and practical models that become apparent as soon as we have more time points, the models are more complex and the models become quite time consuming to estimate because of all the computational costs in estimating those. So, there is a solution and the solution is to use a three-step approach that has been recently devised. And I will discuss this in more details. The advantage of this approach is basically that the measurement models and the structural models are not estimated at the same time, but rather at different steps. The measurement models are estimated and selected in the first step and individuals are assigned to the most likely class based on the posterior membership probability. And after that, we can assess measurement error in latent classes that is the uncertainty in latent class membership. And since this latent class membership is estimated, membership is estimated with error and is uncertain to some degree, it is important to control for this uncertainty to avoid biased results. In the first step, we take individuals in the class membership accounting for measurement errors estimated in the first step, in the previous steps and we can investigate associations between latent classes as well as covariates and install outcomes. But because we are not re-estimated the measurement model at the same time, the first step only concerns associations between latent classes and other variables and not the indicators. So I will provide a practical example. So let's assume that at each time point we have separately estimated these models where there are two latent classes at age 14 and three latent classes at age 15. The issue may be complicated by measurement in virus and in the exercises I provide more guidance on this. Having selected the best measurement models at each time point, we can assign individuals to another latent class based on the posterior probabilities as you can see in this example with the individuals assigned to different classes and the probability of being in that class. So let's focus on age 14. Here we see three individuals have been assigned to latent class experimenters and five are assigned to latent class abstainers. And you can also see the probabilities to be in those respected classes. If we take the three people assigned to experimenters we can calculate the average probability of being in this class if there are experimental members. So that will be 0.79 plus 0.76 plus 0.86 divided by 3. And since these probabilities add to one conversely, the average probability of being an abstainer when people are considered experimenters experimental members is 0.21 plus 0.33 plus 0.23 divided by 3, that is 0.26. We can report these probabilities in a table like this one I report here. And when we consider the number of individuals assigned to each class we can calculate the classification probabilities of being an experimenter if someone is considered an experimental member and this is basically the product of the average probability of being an experimenter if someone is an experimental member by the number of individuals assigned to the experimental class. And this is divided by the same product plus the product of the average probability of being an experimenter if someone is considered an abstainer member by the number of people assigned to abstainer to the abstainers class. So once we have these classification probabilities we can use these to calculate the odds of being an experimenter if someone is considered an experimenter rather than an abstainer. And the logarithm of these odds represent in a single number the uncertainty in assigning participants to the class experimenter. So how much can we be certain that those assigned to experimenters in the experimenter's class are experimenters. So once we have calculated these odds we can use the latent class membership as a nominal variable and use it to estimate latent class membership fixing the uncertainty in this classification to the value of the log odds of being in one class if someone belongs to that class rather than the other class. In other words, we are feeding to the model the information about latent class membership together with the information about their certainty in this classification which is represented by the log odds I calculated before. In this way the measurement model here is fixed it is not estimated anew and we can investigate the associations between latent classes at different time points consider in the measurement model we have models we have selected as optimal. So to summarize I have illustrated the first stages of latent transition analysis firstly we have to investigate the number of classes that adequately explain heterogeneity of behavior at different time points we can then test measurement invariance between classes when these classes appear to be similar. And once we have selected one or a few optimal measurement models we can extract the measurement parameters and use the free-stripe approach to investigate the associations between latent classes across time and also between those classes and other variables as I will discuss in more details in the third presentation. I have highlighted that the advantages of the free-stripe approach lie in the reduction of computation in latent transition models and there are substantial advantages in working with a given measurement model that has a given interpretation and is not re-estimated anew with every analysis. So thank you very much.